Chapter-4 Simple Equations Worksheet

Explanation

Solution:

(i) x + 3 = 0

Here it is given that x + 3=0 and the value of x=3

To find whether the value of x is satisfying the equation, put the value of x=3

Then, left side of the equation is

x+3=3+3=6

But on the right side it is given 0

As we know that 6 ≠ 0

No, the value of x is not satisfying the equation.

(ii) x + 3 = 0

Here it is given that x + 3=0 and the value of x=0

To find whether the value of x is satisfying the equation, put the value of x=0

Then, left side of the equation is

x+3=0+3=3

But on the right side it is given 0

As we know that 3 ≠ 0

No, the value of x is not satisfying the equation.

(iii) x + 3 = 0

Here it is given that x + 3=0 and the value of x=3

To find whether the value of x is satisfying the equation, put the value of x=-3

Then, left side of the equation is

x+3=-3+3=0

But on the right side it is given 0

As we know that 0=0

Yes, the equation is satisfied.

(iv) x – 7 = 1

Here it is given that x-7=1 and the value of x=7

To find whether the value of x is satisfying the equation, put the value of x=7

Then, left side of the equation is

x-7=7-7=0

But on the right side it is given 1

As we know that 0 ≠ 1

No, the value of x is not satisfying the equation.

(v) x – 7 = 1

Here it is given that x-7=1 and the value of x=8

To find whether the value of x is satisfying the equation, put the value of x=8

Then, left side of the equation is

x-7=8-7=1

But on the right side it is given 1

As we know that 1=1

Yes, the value of x is satisfying the equation.

(vi) 5x = 25

Here it is given that 5x=25 and the value of x=0

To find whether the value of x is satisfying the equation, put the value of x=0

Then, left side of the equation is

5x=5×0=0

But on the right side it is given 25

As we know that 0 ≠ 25

No, the value of x is not satisfying the equation.

(vii) 5x = 25

Here it is given that 5x=25 and the value of x=5

To find whether the value of x is satisfying the equation, put the value of x=5

Then, left side of the equation is

5x=5×5=25

But on the right side it is given 25

As we know that 25=25

Yes, the value of x is satisfying the equation.

(viii) 5x = 25

Here it is given that 5x=25 and the value of x= (-5)

To find whether the value of x is satisfying the equation, put the value of x= (-5)

Then, left side of the equation is

5x=5× (-5) = (-25)

But on the right side it is given 25 

As we know that (-25) ≠ 25

No, the value of x is not satisfying the equation.

(ix) m/3 = 2

Here it is given that m/3=2 and the value of m= -6

To find whether the value of m is satisfying the equation, put the value of m= -6

Then, left side of the equation is

m/3= (-6)/3= (-2)

But on the right side it is given 2

As we know that -2 ≠ 2

No, the value of m is not satisfying the equation.

(x) m/3 = 2

Here it is given that m/3=2 and the value of m=0

To find whether the value of m is satisfying the equation, put the value of m=0

Then, left side of the equation is

m/3=0/3=0

But on the right side it is given 2

As we know that 0 ≠ 2

No, the value of m is not satisfying the equation.

(xi) m/3 = 2

Here it is given that m/3=2 and the value of m=6

To find whether the value of m is satisfying the equation put the value of m=6

Then, left side of the equation is

m/3=6/3=2

But on the right side it is given 2

As we know that 2=2

Yes, the value of m is satisfying the equation.

Explanation

Solution:

1. Here it is given that n+5=19 and the value of n=1

To find whether the value of n is satisfying the equation, put the value of n=1

Then, left side of the equation is

=n+5

=1+5

=6

But on the right side it is given 19

As we know that 6 ≠ 19

Therefore, the value of n=1 is not satisfying the equation n+5=19.

2. Here it is given that 7n+5=19 and the value of n= (-2)

To find whether the value of n is satisfying the equation, put the value of n= (-2)

Then, left side of the equation is

=7n+5

=7× (-2) +5

= (-14) +5

= (-9)

But on the right side it is given 19

As we know that (-9) ≠ 19

Therefore, the value of n= (-2) is not satisfying the equation 7n+5=19.

3. Here it is given that 7n+5=19 and the value of n=2

To find whether the value of n is satisfying the equation, put the value of n=2

Then, left side of the equation is

=7n+5

=7×2+5

=14+5

=19

But on the right side it is given 19

As we know that 19=19

Therefore, the value of n=2 is satisfying the equation 7n+5=19.

4. Here it is given that 4p-3=13 and the value of p=1

To find whether the value of p is satisfying the equation, put the value of p=1

Then, left side of the equation is

=4p-3

=4×1-3

=4-3

=1

But on the right side it is given 13

As we know that 1 ≠ 13

Therefore, the value of p=1 is not satisfying the equation 4p-3=13.

5. Here it is given that 4p-3=13 and the value of p= (-4)

To find whether the value of p is satisfying the equation, put the value of p= (-4)

Then, left side of the equation is

=4p-3

=4× (-4) -3

= (-16)-3

= (-19)

But on the right side it is given 13

As we know that (-19) ≠ 13

Therefore, the value of p= (-4) is not satisfying the equation 4p-3=13.

6. Here it is given that 4p-3=13 and the value of p=0

To find whether the value of p is satisfying the equation, put the value of p=0

Then, left side of the equation is

=4p-3

=4×0-3

=0-3

= (-3)

But on the right side it is given 13

As we know that (-3) ≠ 13

Therefore, the value of p=1 is not satisfying the equation 4p-3=13.

3. Solve the following equations by trial-and-error method.

(i) 5p + 2 = 17

(ii) 3m – 14 = 4

Solution:

i) Here, the left side of the equation is 5p+2

Let us suppose that the value of p=0

To find whether the value of p is satisfying the equation, put the value of p=0

Then, left side of the equation is

=5p+2

=5×0+2

=0+2

=2

But on the right side it is given 17

As we know that 2 ≠ 17

Therefore, the value of p=0 is not satisfying the equation 5p+2=17.

Now, let us suppose that the value of p=1

To find whether the value of p is satisfying the equation, put the value of p=1

Then, left side of the equation is

=5p+2

=5×1+2

=5+2

=7

But on the right side it is given 17

As we know that 7 ≠ 17

Therefore, the value of p=1 is not satisfying the equation 5p+2=17.

Now, let us suppose that the value of p=2

To find whether the value of p is satisfying the equation, put the value of p=2

Then, left side of the equation is

=5p+2

=5×2+2

=10+2

=12

But on the right side it is given 17

As we know that 12 ≠ 17

Therefore, the value of p=2 is not satisfying the equation 5p+2=17.

Now, let us suppose that the value of p=3

To find whether the value of p is satisfying the equation, put the value of p=3

Then, left side of the equation is

=5p+2

=5×3+2

=15+2

=17

On the right side it is given 17

As we know that 17=17

Therefore, the value of p=3 is satisfying the equation 5p+2=17.

ii) Here, the left side of the equation is 3m-14

Let us suppose that the value of m=5

To find whether the value of m is satisfying the equation, put the value of m=5

Then, left side of the equation is

=3m-14

=3×5-14

=15-14

=1

But on the right side it is given 4

As we know that 1 ≠ 4

Therefore, the value of m=5 is not satisfying the equation 3m-14=4.

Now, let us suppose that the value of m=6

To find whether the value of m is satisfying the equation, put the value of m=6

Then, left side of the equation is

=3m-14

=3×6-14

=18-14

=4

On the right side it is given 4

As we know that 4=4

Therefore, the value of m=6 is satisfying the equation 3m-14=4.

Explanation

Solution:

i) Here, the left side of the equation is 5p+2

Let us suppose that the value of p=0

To find whether the value of p is satisfying the equation, put the value of p=0

Then, left side of the equation is

=5p+2

=5×0+2

=0+2

=2

But on the right side it is given 17

As we know that 2 ≠ 17

Therefore, the value of p=0 is not satisfying the equation 5p+2=17.

Now, let us suppose that the value of p=1

To find whether the value of p is satisfying the equation, put the value of p=1

Then, left side of the equation is

=5p+2

=5×1+2

=5+2

=7

But on the right side it is given 17

As we know that 7 ≠ 17

Therefore, the value of p=1 is not satisfying the equation 5p+2=17.

Now, let us suppose that the value of p=2

To find whether the value of p is satisfying the equation, put the value of p=2

Then, left side of the equation is

=5p+2

=5×2+2

=10+2

=12

But on the right side it is given 17

As we know that 12 ≠ 17

Therefore, the value of p=2 is not satisfying the equation 5p+2=17.

Now, let us suppose that the value of p=3

To find whether the value of p is satisfying the equation, put the value of p=3

Then, left side of the equation is

=5p+2

=5×3+2

=15+2

=17

On the right side it is given 17

As we know that 17=17

Therefore, the value of p=3 is satisfying the equation 5p+2=17.

ii) Here, the left side of the equation is 3m-14

Let us suppose that the value of m=5

To find whether the value of m is satisfying the equation, put the value of m=5

Then, left side of the equation is

=3m-14

=3×5-14

=15-14

=1

But on the right side it is given 4

As we know that 1 ≠ 4

Therefore, the value of m=5 is not satisfying the equation 3m-14=4.

Now, let us suppose that the value of m=6

To find whether the value of m is satisfying the equation, put the value of m=6

Then, left side of the equation is

=3m-14

=3×6-14

=18-14

=4

On the right side it is given 4

As we know that 4=4

Therefore, the value of m=6 is satisfying the equation 3m-14=4.

Explanation

Solution:

i) The sum of the number x and 4 is 9

Sum means addition which can be symbolized by “+”

So, we can write x+4

And the summation is equal to 9

So, x+4=9

(ii) Here by subtracting 2 from y we can obtain 8

Subtraction can be symbolized as “- “

So, we can write y-2

And this is equal to 8

So, y-2=8

(iii) Here it is given that ten times a is 70

Now Ten times a means multiplication of 10 with a 

Which is 10×a

Now, this is equal to 70Three

So, 10×a=70

(iv) here it is given that number b divided by 5 gives 6

b divided by 5 can be written as b/5

and this will give 6

so, (b/5) =6

(v) Here three-fourth of t is 15

Now, three fourth means ¾, and it is three-fourth of t

Which means ¾t, and this value is equal to 15

So, ¾t = 15

(vi) Here seven times m plus 7 gets us 77

Now, seven times m plus seven is equal to 7m+7

And this value is equal to 77

So, 7m+7=77

vi) Here it is given that one-fourth of a number x minus 4 gives 4

Now, one-fourth of a number x minus 4 is equal to x/4-4

And this value is equal to 4

So, x/4-4=4

(viii) Here it is given that if we take out 6 from 6 times y, we get 60.

Now, 6 times y minus 6 can be written as 6y-6

And this value will be equal to 60

So, 6y-6=60

(ix) Here it is given that if we add 3 to one-third of z, we get 30

Now, 3 added to one-third of z can be written as 3+z/3

And this value will be equal to 30

So, 3+z/3=30

Explanation

Solution:

i)Here it is given that by adding p and 4

The value we obtain will be equal to 15

(ii)Here it is given that by subtracting 7 from m

The value we obtained will be equal to 3.

(iii) Here it is given that two times of the number m

Will be equal to 7.

(iv) Here it is given that one-fifth of the number m

Will be equal to 3.

(v) Here it is given that Three-fifth of the number m 

Will be equal to 6.

(vi) Here it is given that by adding 4 to Three times p

The value obtained will be equal to 25.

(vii) Here it is given that by subtracting 2 from Four times p

The value obtained will be equal to 18.

(viii) Here it is given that y adding 2 to one-half of the number p

The value obtained will be equal to 8.

Solution: 

i) Here in the question, it is given that

Number of Parmit’s marbles = m

Then, from the question 7 marbles Irfan has which is more than five times the marbles Parmit has.

= 5 × Number of Parmit’s marbles + 7 = Total number of marbles Irfan having

= (5 × m) + 7 = 37

= 5m + 7 = 37

So, the equation we obtained is 5m+7=37.

(ii) Here in the question, it is given that

Take Laxmi’s age = y years old

Then, Lakshmi’s father is 49 years old and he is 4 years older than three times her age.

= 3 × Laxmi’s age + 4 = Age of Lakshmi’s father

= (3 × y) + 4 = 49

= 3y + 4 = 49

So, the equation we obtained is 3y+4=49.

(iii) Here in the question, it is given that

The highest score in the class is 87

Take the lowest score as l.

= 2 × Lowest score + 7 = Highest score in the class

= (2 × l) + 7 = 87

= 2l + 7 = 87

So, the equation obtained is 2l+7=87.

(iv) Here in the question, it is given that

To take the base angle as b.

And as we know that the sum of all the three angles of a triangle is 180o

Then, 

Vertex angle = 2 × base angle = 2b

= b + b + 2b = 180o

= 4b = 180o

So, the equation we obtained is 4b = 180

Explanation

Solution:

i) Here it is given that by subtracting 1 from the number x we obtained 0.

Now, here we need to make one side only the variable number, we can do this by adding 1 to both the side of the equation. 

By doing this, we get

= x – 1 + 1 = 0 + 1

= x = 1

So, the value of x is 1.

(b)Here it is given that by adding 1 in the number x we obtained 0.

Now, here we need to make one side only the variable number, we can do this by subtracting 1 from both the side of the equation. 

By doing this, we get

= x + 1 – 1 = 0 – 1

= x = – 1

So, the value of x is -1.

(c)Here it is given that by subtracting 1 from the number x we obtained 5.

Now, here we need to make one side only the variable number, we can do this by adding 1 to both the side of the equation. 

By doing this, we get

= x – 1 + 1 = 5 + 1

= x = 6

So, the value of x is 6.

(d)Here it is given that by adding 6 in the number x we obtained 2.

Now, here we need to make one side only the variable number, we can do this by subtracting 6 from both the side of the equation. 

By doing this, we get

= x + 6 – 6 = 2 – 6

= x = – 4

So, the value of x is -4.

(e)Here it is given that by subtracting 4 from the number y we obtained -7.

Now, here we need to make one side only the variable number, we can do this by adding 4 to both the side of the equation. 

By doing this, we get

= y – 4 + 4 = – 7 + 4

= y = – 3

So, the value of y is -3.

(f)Here it is given that by subtracting 4 from the number y we obtained 4.

Now, here we need to make one side only the variable number, we can do this by adding 4 to both the side of the equation. 

By doing this, we get

= y – 4 + 4 = 4 + 4

= y = 8

So, the value of x is 8.

(g)Here it is given that by adding 4 in the number y we obtained 4.

Now, here we need to make one side only the variable number, we can do this by subtracting 4 from both the side of the equation. 

By doing this, we get

= y + 4 – 4 = 4 – 4

= y = 0

So, the value of x is 0.

(h)Here it is given that by adding 4 in the number y we obtained -4.

Now, here we need to make one side only the variable number, we can do this by subtracting 4 from both the side of the equation. 

By doing this, we get

= y + 4 – 4 = – 4 – 4

= y = – 8

So, the value of x is -8.

Explanation

a) Here it is given that by multiplying 3 to the number I we obtained 42.

Now, here we need to make one side only the variable number, we can do this by dividing both the side of the equation by 3. 

By doing this, we get

= 3l/3 = 42/3

= l = 14

So, the value of I is 14.

(b) Here it is given that by dividing 2 to the number b we obtained 6.

Now, here we need to make one side only the variable number, we can do this by multiplying both the side of the equation by 2. 

By doing this, we get

= b/2 × 2= 6 × 2

= b = 12

So, the value of b is 12.

c) Here it is given that by dividing 7 to the number p we obtained 4.

Now, here we need to make one side only the variable number, we can do this by multiplying both the side of the equation by 7. 

By doing this, we get

= p/7 × 7= 4 × 7

= p = 28

So, the value of p is 28.

(d) Here it is given that by multiplying 4 to the number x we obtained 25.

Now, here we need to make one side only the variable number, we can do this by dividing both the side of the equation by 4. 

By doing this, we get

= 4x/4 = 25/4

= x = 25/4

So, the value of x is 25/4.

(e) Here it is given that by multiplying 8 to the number y we obtained 36.

Now, here we need to make one side only the variable number, we can do this by dividing both the side of the equation by 8. 

By doing this, we get

= 8y/8 = 36/8

= x = 9/2

So, the value of x is 9/2.

(f) Here it is given that by dividing 3 to the number z we obtained 5/4.

Now, here we need to make one side only the variable number, we can do this by multiplying both the side of the equation by 3. 

By doing this, we get

= (z/3) × 3 = (5/4) × 3

= x = 15/4

So, the value of z is 15/4.

(g)Here it is given that by dividing 5 to the number a we obtained 7/15.

Now, here we need to make one side only the variable number, we can do this by multiplying both the side of the equation by 5. 

By doing this, we get

= (a/5) × 5 = (7/15) × 5

= a = 7/3

So, the value of a is 7/3.

(h) Here it is given that by multiplying 20 to the number t we obtained -10.

Now, here we need to make one side only the variable number, we can do this by dividing both the side of the equation by 20. 

By doing this, we get

= 20t/20 = -10/20

= t = – ½

So, the value of t is – ½.

Explanation

Solution:

a)Here it is given that by multiplying 20 to the number n and subtracting 2 we obtained 46.

Now, here we need to make one side only the variable number, so first we add 2 on both the side of the equation then dividing both the side of the equation by 3. 

By doing this, we get

= 3n – 2 + 2 = 46 + 2

= 3n = 48

= 3n/3 = 48/3

= n = 16

So, the value of n is 16.

(b) Here it is given that by multiplying 5 to the number m and adding 7 we obtained 17.

Now, here we need to make one side only the variable number, so first we subtract 7 on both the side of the equation then dividing both the side of the equation by 5. 

By doing this, we get

= 5m + 7 – 7 = 17 – 7

= 5m = 10

= 5m/5 = 10/5

= m = 2

So, the value of m is 2.

(c) Here it is given that by multiplying 20 to the number p and dividing it by 3 we obtained 40.

Now, here we need to make one side only the variable number, so first we multiply 3 on both the side of the equation then dividing both the side of the equation by 20. 

By doing this, we get

= (20p/3) × 3 = 40 × 3

= 20p = 120

= 20p/20 = 120/20

= p = 6

So, the value of p is 6.

(d) Here it is given that by multiplying 3 to the number p and dividing it by 10 we obtained 6.

Now, here we need to make one side only the variable number, so first we multiply 10 on both the side of the equation then dividing both the side of the equation by 3. 

By doing this, we get

= (3p/10) × 10 = 6 × 10

= 3p = 60

= 3p/3 = 60/3

= p = 20

So, the value of p is 20.

Explanation

Solution:

• a)Here it is given that by multiplying 10 to the number p we obtained 100.

Now, here we need to make one side only the variable number, we can do this by dividing both the side of the equation by 10. 

By doing this, we get

= 10p/10 = 100/10

= p = 10

So, the value of p is 10.

(b) Here it is given that by multiplying 10 to the number p and adding 10 we obtained 100.

Now, here we need to make one side only the variable number, so first we subtract 10 on both the side of the equation then dividing both the side of the equation by 10. 

By doing this, we get

= 10p + 10 – 10 = 100 – 10

= 10p = 90

= 10p/10 = 90/10

= p = 9

So, the value of p is 9.

(c) Here it is given that by dividing 4 to the number p we obtained 5.

Now, here we need to make one side only the variable number, we can do this by multiplying both the side of the equation by 4. 

By doing this, we get

= p/4 × 4 = 5 × 4

= p = 20

So, the value of p is 20.

(d) Here it is given that by dividing -3 to the number p we obtained 5.

Now, here we need to make one side only the variable number, we can do this by multiplying both the side of the equation by -3. 

By doing this, we get

= – p/3 × (- 3) = 5 × (- 3)

= p = – 15

So, the value of p is -15.

(e) Here it is given that by multiplying 3 to the number p and dividing it by 4 we obtained 6.

Now, here we need to make one side only the variable number, so first we multiply 4 on both the side of the equation then dividing both the side of the equation by 3. 

By doing this, we get

= (3p/4) × (4) = 6 × 4

= 3p = 24

= 3p/3 = 24/3

= p = 8

So, the value of p is 8.

(f) 

Here it is given that by multiplying 3 to the number s we obtained -9.

Now, here we need to make one side only the variable number, we can do this by divide both the side of the equation by 3. 

By doing this, we get

= 3s/3 = -9/3

= s = -3

So, the value of s is -3.

(g) Here it is given that by multiplying 3 to the number s and adding 12 we obtained 0.

Now, here we need to make one side only the variable number, so first we subtract 12 on both the side of the equation then dividing both the side of the equation by 3. 

By doing this, we get

= 3s + 12 – 12 = 0 – 12

= 3s = -12

= 3s/3 = -12/3

= s = – 4

So, the value of s is – 4.

(h) Here it is given that by multiplying 3 to the number s we obtained 0.

Now, here we need to make one side only the variable number, we can do this by dividing both the side of the equation by 3. 

By doing this, we get

= 3s/3 = 0/3

= s = 0

So, the value of s is 0.

(i) 

Here it is given that by multiplying 2 to the number q we obtained 6.

Now, here we need to make one side only the variable number, we can do this by dividing both the side of the equation by 2. 

By doing this, we get

= 2q/2 = 6/2

= q = 3

So, the value of q is 3.

(j) Here it is given that by multiplying 2 to the number q and subtracting 6 we obtained 0.

Now, here we need to make one side only the variable number, so first we add 6 on both the side of the equation then dividing both the side of the equation by 2. 

By doing this, we get

= 2q – 6 + 6 = 0 + 6

= 2q = 6

= 2q/2 = 6/2

= q = 3

So, the value of q is 3.

(k) Here it is given that by multiplying 2 to the number q and adding 6 we obtained 0.

Now, here we need to make one side only the variable number, so first we subtract 6 on both the side of the equation then dividing both the side of the equation by 2. 

By doing this, we get

= 2q + 6 – 6 = 0 – 6

= 2q = – 6

= 2q/2 = – 6/2

= q = – 3

So, the value of q is –3.

(l) Here it is given that by multiplying 2 to the number q and adding 6 we obtained 12.

Now, here we need to make one side only the variable number, so first we subtract 6 on both the side of the equation then dividing both the side of the equation by 2. 

By doing this, we get

= 2q + 6 – 6 = 12 – 6

= 2q = 6

= 2q/2 = 6/2

= q = 3

So, the value of q is 3.

Explanation

Solution:

a)Here it is given that by multiplying 2 to the number y and adding 5/2 we obtained 37/2.

Now, take 5/2 which is on left-hand side to the right-hand side so that it will become -5/2. 

By doing this, we get

= 2y = (37/2) – (5/2)

= 2y = (37-5)/2

= 2y = 32/2

Now to obtain the value of y divide both the side of the equation by 2.

By doing this, we get

= 2y/2 = (32/2)/2

= y = (32/2) × (1/2)

= y = 32/4

= y = 8

So, the value of y is 8.

(b) Here it is given that by multiplying 5 to the number t and adding 28 we obtained 10.

Now, take 28 which is on left-hand side to the right-hand side so that it will become -28. 

By doing this, we get

= 5t = 10 – 28

= 5t = – 18

Now to obtain the value of t divide both the side of the equation by 5.

By doing this, we get

= 5t/5= -18/5

= t = -18/5

So, the value of t is -18/5.

(c) Here it is given that by dividing 5 to the number a and adding 3 we obtained 2.

Now, take 3 which is on left-hand side to the right-hand side so that it will become -3. 

By doing this, we get

= a/5 = 2 – 3

= a/5 = – 1

Now to obtain the value of a multiply both the side of the equation by 5.

By doing this, we get

= (a/5) × 5= -1 × 5

= a = -5

So, the value of a is -5.

(d) Here it is given that by dividing 4 to the number q and adding 7 we obtained 5.

Now, take 7 which is on left-hand side to the right-hand side so that it will become -7. 

= q/4 = 5 – 7

= q/4 = – 2

By doing this, we get

Now to obtain the value of q multiply both the side of the equation by 5.

By doing this, we get

= (q/4) × 4= -2 × 4

= q = -8

So, the value of q is -8.

(e)Here it is given that by dividing 2 to the number x and multiply by 5 we obtained -5.

Now, multiply by 2 on left-hand side and right-hand side. 

By doing this, we get

= (5x/2) × 2 = – 5 × 2

= 5x = – 10

Now to obtain the value of x divide both the side of the equation by 5.

By doing this, we get

= 5x/5 = -10/5

= x = -2

So, the value of x is -2.

(f) Here it is given that by dividing 2 to the number x and multiply by 5 we obtained 25/4.

Now, multiply by 2 on left-hand side and right-hand side. 

By doing this, we get

= (5x/2) × 2 = (25/4) × 2

= 5x = (25/2)

Now to obtain the value of x divide both the side of the equation by 5.

By doing this, we get

= 5x/5 = (25/2)/5

= x = (25/2) × (1/5)

= x = (5/2)

So, the value of x is 5/2.

(g) Here it is given that by multiplying 7 to the number m and adding 19/2 we obtained 13.

Now, take 19/2 which is on left-hand side to the right-hand side so that it will become -19/2. 

By doing this, we get

= 7m = 13 – (19/2)

= 7m = (26 – 19)/2

= 7m = 7/2

Now to obtain the value of m multiply both the side of the equation by 5.

By doing this, we get

= 7m/7 = (7/2)/7

= m = (7/2) × (1/7)

= m = ½

So, the value of m is ½.

(h) Here it is given that by multiplying 6 to the number z and adding 10 we obtained -2.

Now, take 10 which is on left-hand side to the right-hand side so that it will become -10. 

By doing this, we get

= 6z = -2 – 10

= 6z = – 12

Now to obtain the value of m multiply both the side of the equation by 5.

By doing this, we get

= 6z/6 = -12/6

= z = – 2

So, the value of z is -2.

(i) Here it is given that by dividing 2 to the number I and multiply by 5 we obtained 2/3.

Now, multiply by 2 on left-hand side and right-hand side. 

By doing this, we get 

= (3l/2) × 2 = (2/3) × 2

= 3l = (4/3)

Now to obtain the value of I divide both the side of the equation by 3.

By doing this, we get

= 3l/3 = (4/3)/3

= l = (4/3) × (1/3)

= I = (4/9)

So, the value of I is 4/9.

(j)Here it is given that by multiplying 2/3 to the number b and subtracting 5 we obtained 3.

Now, take -5 which is on left-hand side to the right-hand side so that it will become 5. 

By doing this, we get

= 2b/3 = 3 + 5

= 2b/3 = 8

Now to obtain the value of q multiply both the side of the equation by 3.

By doing this, we get

= (2b/3) × 3= 8 × 3

= 2b = 24

Now to obtain the value of b divide both the side of the equation by 2.

By doing this, we get

= 2b/2 = 24/2

= b = 12

So, the value of b is 12.

Explanation

Solution:

a)Here to find the value of the x divide both the side of the equation by 2.

= (2(x + 4))/2 = 12/2

= x + 4 = 6

Now subtract 4 from both the side of the equation.

= x = 6 – 4

= x = 2

So, the value of x is 2.

(b) Here to find the value of the n divide both the side of the equation by 3.

= (3(n – 5))/3 = 21/3

= n – 5 = 7

Now, take 5 on the left-hand side to the right-hand side.

= n = 7 + 5

= n = 12

So, the value of n is 12.

(c) Here to find the value of the n divide both the side of the equation by 3.

= (3(n – 5))/3 = – 21/3

= n – 5 = -7

Now, take 5 on the left-hand side to the right-hand side.

= n = – 7 + 5

= n = – 2

So, the value of n is -2.

(d)Here to find the value of the x divide both the side of the equation by -4.

= (-4(2 + x))/ (-4) = 8/ (-4)

= 2 + x = -2

Now, take 2 on the left-hand side to the right-hand side.

= x = -2 – 2

= x = – 4

So, the value of x is -4.

(e) Here to find the value of the x divide both the side of the equation by 4.

= (4(2 – x))/ 4 = 8/ 4

= 2 – x = 2

Now, take 2 on the left-hand side to the right-hand side.

= – x = 2 – 2

= – x = 0

= x = 0

So, the value of x is 0.

Explanation

Solution:

a)Here to find the value of the p divide both the side of the equation by 5.

= 4/5 = (5(p – 2))/5

= 4/5 = p -2

Now, take 2 on the right-hand side to the left-hand side.

= (4/5) + 2 = p

= (4 + 10)/ 5 = p

= p = 14/5

So, the value of p is 14/5.

(b) Here to find the value of the p divide both the side of the equation by 5.

= -4/5 = (5(p – 2))/5

= -4/5 = p -2

Now, take 2 on the right-hand side to the left-hand side.

= – (4/5) + 2 = p

= (- 4 + 10)/ 5 = p

= p = 6/5

So, the value of p is 6/5.

(c) Here, we can move 4 from the right-hand side to the left-hand side.

= 16 – 4 = 3(t + 2)

= 12 = 3(t + 2)

Now to find the value of the t divide both the side of the equation by 3.

= 12/3 = (3(t + 2))/ 3

= 4 = t + 2

Now subtract 2 from both the side of the equation.

= 4 – 2 = t

= t = 2

So, the value of t is 2.

(d) Here, we can move 4 from the left-hand side to the right-hand side.

= 5(p – 1) = 34 – 4

= 5(p – 1) = 30

Now to find the value of the p divide both the side of the equation by 5.

= (5(p – 1))/ 5 = 30/5

= p – 1 = 6

Now add 1 to both the side of the equation.

= p = 6 + 1

= p = 7

So, the value of p is 7.

(e) Here, we can move 16 from the right-hand side to the left-hand side.

= 0 – 16 = 4(m – 6)

= – 16 = 4(m – 6)

Now to find the value of the m divide both the side of the equation by 4.

= – 16/4 = (4(m – 6))/ 4

= – 4 = m – 6

Now add 6 to both the side of the equation.

= – 4 + 6 = m

= m = 2

So, the value of m is 2.

Explanation

Solution:

a)Here the equation given to us is x=2,

We have to create 3 equations from this equation.

Let’s create our first equation by multiplying both the side by 3.

= 3x = 6 … [equation 1]

To create second equation, add 5 on each side of the equation,

= 3x + 5 = 6 + 5

= 3x + 5 = 11 … [equation 2]

For third equation, divide both sides by 3.

= (3x/3) + (5/3) = (11/3)

= x + (5/3) = (11/3) … [equation 3]

(b) Here the equation given to us is x= -2,

We have to create 3 equations from this equation.

Let’s create our first equation by multiplying both the side by 3.

= 3x = -6 … [equation 1]

To create second equation, add 5 on each side of the equation,

= 3x + 5 = -6 + 5

= 3x + 5 = -1 … [equation 2]

For third equation, divide both sides by 3.

= (3x/3) + (5/3) = (-1/3)

= x + (5/3) = (-1/3) … [equation 3

Explanation

Solution:

a)Here it is given that by adding 4 to eight times a number it will become 60.

So, let’s suppose that the number is y.

Eight times a number = 8y

Now, according to the condition given in the question we can write,

= 8y + 4 = 60

We get the required equation.

Now, to solve the equation subtract 4 from both the side of the equation.

= 8y = 60 – 4

= 8y = 56

To find the value of y, divide both the sides of the equation by 8.

= (8y/8) = 56/8

= y = 7

So, the equation is 8y + 4 = 60 and the value of y = 7.

(b) Here it is given that by subtracting 4 from one-fifth of a number it will become 3.

So, let’s suppose that the number is y.

One-fifth of a number = (1/5) y = y/5

Now, according to the condition given in the question we can write,

= y/5 - 4 = 3

We get the required equation.

Now, to solve the equation add 4 to both the side of the equation.

= y/5 = 3 + 4

= y/5 = 7

To find the value of y, multiply both the sides of the equation by 5.

= (5y/5) = 7×5

= y = 35

So, the equation is y/5 - 4 = 3 and the value of y = 35.

(c) Here it is given that by adding 4 to three-fourth of a number it will give 21.

So, let’s suppose that the number is y.

Three-fourth of a number = (3/4) y = 3y/4

Now, according to the condition given in the question we can write,

= 3y/4 + 3 = 21

We get the required equation.

Now, to solve the equation subtract 3 from both the side of the equation.

= 3y/4 =21 - 3

= 3y/4 = 18

To find the value of y, multiply both the sides of the equation by 4 and simultaneously divide them by 3.

= (3y/4) × 4 = 18 × 4

= 3y = 72

= (3y/3) = 72/3

= y = 24

So, the equation is 3y/4 + 3 = 21 and the value of y = 24.

(d) Here it is given that by subtracting 11 from twice a number it will give 15.

So, let’s suppose that the number is y.

Twice of a number = 2y

Now, according to the condition given in the question we can write,

= 2y - 11 = 15

We get the required equation.

Now, to solve the equation add 11 to both the side of the equation.

= 2y = 15+11

= 2y = 26

To find the value of y, divide both the sides of the equation by 2.

= (2y/2) = 26/2

= y = 13

So, the equation is 2y - 11 = 15 and the value of y = 13.

(e) Here it is given that Munna subtracted thrice the number of notebooks ha has from 50.

So, let’s suppose that the number of notebooks is y.

Thrice the number of notebooks = 3y

Now, according to the condition given in the question we can write,

= 50 - 3y = 8

We get the required equation.

Now, to solve the equation subtract 50 from both the side of the equation.

= -3y = 8 - 50

= -3y = -42

To find the value of y, divide both the sides of the equation by -3.

= y = (-42)/ (-3)

= y = 14

So, the equation is 50 - 3y = 8 and the value of y = 14.

(f) Here it is given that Ibenhal first adding 19 to the number then dividing whole number by 5 to get 8.

So, let’s suppose that the number is y.

Adding 19 to the number then dividing whole sum by 5= (y+19)/5.

Now, according to the condition given in the question we can write,

= (y+19)/5=8

We get the required equation.

Now, to solve the equation multiply 5 on both the side of the equation.

= ((y + 19)/5) × 5 = 8 × 5

= y + 19 = 40

To find the value of y, subtract 19 from both the sides of the equation.

= y = 40 – 19

= y = 21

So, the equation is (y+19)/5=8 and the value of y = 21.

(g) Here it is given that by subtracting 7 from 5/2 of a number it will become 23.

So, let’s suppose that the number is y.

5/2 of a number = (5/2) y = 5y/2

Now, according to the condition given in the question we can write,

= 5y/2 - 7 = 23

We get the required equation.

Now, to solve the equation add 7 to both the side of the equation.

= 5y/2 = 23 + 7

= 5y/2 = 30

To find the value of y, multiply both the sides of the equation by 2 and simultaneously divide it by 5.

= ((5/2) y) × 2 = 30 × 2

= 5y = 60

= 5y/5 = 60/5

= y = 12

So, the equation is 5y/2 - 7 = 23 and the value of y = 12.

Explanation

Solution:

a)The highest score in the class is 87 and let’s suppose that the lowest marks in the class is y.

Here it is given that by adding 7 to twice the lowest marks will be equal to the highest marks in the class.

Twice of lowest marks = 2y

Now, according to the condition given in the question we can write,

= 2y + 7 = 87

We get the required equation.

Now, to solve the equation subtract 7 from both the side of the equation.

= 2y = 87 - 7

= 2y = 80

To find the value of y, divide both the sides of the equation by 2.

= 2y/2 = 80/2

= y = 40

So, the equation is 2y + 7 = 87 and the value of y = 40.

Therefore, the lowest score in the class is 40.

(b) As we know that in an isosceles triangle the base angles are same and from the properties of the triangle, we know that the sum of angles 180o

So, Let’s suppose that the base angle be x.

= x + x + 40o = 180o

= 2x + 40 = 180o

Now, to obtain the value of x subtract 40 from both the side of the equation and after that divede the obtained equation by 2.

= 2x + 40 - 40 = 180 – 40

= 2x = 140

= 2x/2 = 140/2

= x = 70o

So, the obtained base angle of an isosceles triangle is 70o.

(c) Here it is given that run scored by Sachin is twice than the run score by Rahul and the together score runs two short of a double century,

Let’s suppose that the runs score by the Rahul is x.

So, the run score by the Sachin would be 2x.

Now, according to the condition given in the question we can write,

= 2x + x = 200 – 2

=3x = 198

We get the required equation.

Now, to solve the equation divide both the side of the equations by 3.

= 3x/3 = 198/3

= x = 66

So, the runs score by Rahul is 66.

And the runs score by Sachin is 2x = 2 × 66 = 132

Explanation

Solution:

I)Here it is given that Irfan has 37 marbles which is 7 marbles more than five times the marble Parmit.

So, let’s suppose that Parmit has x marbles.

We can write from the condition given in the equation

= 5 × Number of Parmit’s marbles + 7 = Number of Irfan’s marbles

= (5 × x) + 7 = 37

= 5x + 7 = 37

Now to solve the obtained equation subtract 7 from both the side.

= 5x +7 -7 = 37 – 7

= 5x = 30

To find the value of x divide both sides by 5.

= 5x/5 = 30/5

= x = 6

So, there are total 6 marbles Permit has.

(ii) Here the age of Laxmi’s father is given as 49 years.

Let’s suppose that the age of Laxmi is x.

Now, from the condition given in the question, the age of Laxmi’s father is 4 more than three times Laxmi’s age,

So, we can write 

= 3 × Laxmi’s age + 4 = Age of Lakshmi’s father

= (3 × x) + 4 = 49

= 3x + 4 = 49

To solve the obtained equation, subtract 4 from both the side.

= 3x +4 -4 = 49 – 4

= 3x = 45

To obtain the value of x divide both sides by 3.

= 3x/3 = 45/3

= x = 15

Hence, the age of Lakshmi is 15 years.

(iii) Here the number of non-fruit tree are given as 77.

So, let’s suppose that the number of fruit tree are x.

Now, the condition given in the question, number of non-fruit tree was two more than three times the number of fruit trees.

So, we can writer

3 × number of fruit trees + 2 = number of non-fruit trees

= 3x + 2 = 77

To solve the obtained equation, subtract 2 from both the side.

=3x +2 -2 = 77 – 2

= 3x = 75

To obtain the value of x divide both sides by 3.

= 3x/3 = 75/3

= x = 25

Hence, the number of fruit trees planted in the village garden was 25.

Solution:

Here in the question it is given that by taking seven times of a number and adding 50 to it we will obtain reach to triple century but also need to add 40 to reach up to 300.

Let’s suppose that the number is x.

So, by taking seven times over and adding fifty to it will give 7x + 50

But to reach up to triple century we still need to add forth

= (7x + 50) + 40 = 300

= 7x + 50 + 40 = 300

= 7x + 90 = 300

To solve the obtained equation, subtract 90 from both the side.

= 7x = 300 – 90

= 7x = 210

To obtain the value of x divide both sides by 7.

= 7x/7 = 210/7

= x = 30

So, the number is 30.