Chapter-4 Linear Equations in One Variable exampler

Explanation:

(c) 4x + 7 = x + 2

Here, let's take option C.

Not in the option C the equation is given to us is

4x+7=x+2

Now, take 7 from left side to right side and x from right side to left side,

4x – x = 2 – 7

3x = – 5

X = -5/3

We know that, -5/3 is neither a fraction nor an integer.

Explanation:

(c) x = -b/a

Here, in the question, the equation is given to us and that is ax+b=0

Now, we have to find the value of x.

So, to find the value of x, take the b from left side to right side and than a on the left side if in multiplication which will be in division on the right hand side,

ax = -b

x = -b/a

Explanation:

(c) a rational number

Here, in the above question, the equation is given to us and that is 8x-3=25+17x

Now, we have to find the value of x and based on that value we have to divide which type of value x have.

So, take -3 from left to right and 17x from right to left,

8x – 17x = 25 + 3

-9x = 28

X = -28/9

Hence, x is a rational number.

Explanation:

(a) Transposition

Here, in the above question, we have asked to give the proper name for a process.

We know that, when we shift a number from one side to another, it is known as transposition.

Explanation:

(b) -13/19

Here, in the above question, we have given as equation which is (5x/3) – 4 = (2x/5)

Not, first we need to find the value of x.

So, to find the value of x we need to solve the above equation,

(5x/3) – (2x/5) = 4

(25x – 6x)/15 = 4

19x = 4 × 15

19x = 60

X = 60/19

Now, we have to find the value of  2x -7.

So, to find the value of the above equation, substitute the value of x obtained from the first equation in the above equation.

= (2 × (60/19)) – 7

= (120/19) – 7

= (120 – 133)/19

= – 13/19

Explanation:

(c) 5

 Here, in the above question, we have to find the value of x fir which the value of both the above mentioned equation will become same.

So, first take both the equation equal to each other

3x – 4 = 2x + 1

Now, take all the variable one side and the numericals values on other side,

3x – 2x = 1 + 4

X = 5

Hence, the value of x is 5.

Explanation:

(a) positive

Here, in the above question, the nature of a and b is give to us and that is both are positive integers.

So, if we put the value of a and b in the given equation, we get the value of x as positive integer only.

Let's take an example,

Let a = 7, b = 9

Then, ax = b

7x = 9

X = 9/7

Explanation:

(c) only one variable with power 1.

We know that, linear equation in one variable has only one variable term with the power 1.

Explanation:

(d) 1 + z

We know that, linear equation in one variable has only one variable term with the power 1.

So, from the above given options, we can say that option d has variable term with the power one.

Explanation:

(a) Only one solution

We know that, linear equation in one variable has only one variable term with the power 1.

As the power of variable term is one, the solution is also going to be one only.

Explanation:

(b) 1/15

Here, in the above question, we have given an equation which is 1/3 + S = 2/5.

Now, to solve the above equation, take all the variable term on one side and the numerical values in the other side,

S = 2/5 – 1/3

S = (6 – 5)/15

S = 1/15

Explanation:

(c) (¾)2

Here, in the above question, we have given an equation which is (-4/3)y = -¾.

Now, to solve the above equation, take all the variable term on one side and the numerical values in the other side,

Y = – ¾ × -¾

Y = 9/16

Y = (3 × 3)/(4 × 4)

Y = 32/42

Y = (¾)2

Explanation:

(a) 11b + 30

Here, in the above question, we have given the conditions to create a equation,

So, in the question, the digit at units place is given as b and the digit in the tens place of a two digit number is 3 more than the digit in the units place = 3 + b

So, we know that the number can be written in the form = 10 (3 + b) + b

= 30 + 10b + b

= 30 + 11b

Explanation:

(d) 3(x + 3)

Here, in the above question, agreed of both Shilpa and Arpita is given in the form of relation.

Now, we have to convert this relation into the equation form.

So, from the question, let's suppose that

Shilpa’s age three years ago was x

Then, Shilpa’s present age is = x + 3

Hence, Arpita’s present age is thrice of Shilpa which means we can write 

= 3 (x + 3)

Explanation:

(a) 112

Here, we have to add three such consecutive multiply of 7 so that it will become 357.

So, let's suppose that the three consecutive multiples of 7 are 7x, (7x + 7), (7x + 14).

Where, x is a natural number.

Now, as per the condition given in the question,

7x + (7x + 7) + (7x + 14) = 357

21x + 21 = 357

21(x + 1) = 357

(21(x + 1))/21 = 357/21

X + 1 = 17

X = 17 – 1

X = 16

Hence, the smallest multiple of 7 is,

7 × 16 = 112.

In questions 16 to 32, fill in the blanks to make each statement true.

Explanation:

In a linear equation, the highest power of the variable appearing in the equation is one.

We know that, linear equation in one variable has only one variable term with the power 1.

Explanation:

The solution of the equation 3x – 4 = 1 – 2 x is 1.

Here, in the above question, equation in one variable is given to us, which we have to solve and find the value of x.

So, let's solve the above equation,

3x – 4 = 1 – 2

3x – 4 = – 1

3x = -1 + 4

X = 3/3

X = 1

Hence, the value of x is 1.

Explanation:

The solution of the equation 2y = 5y – 18 5 is (6/5).

Here, in the above question, equation in one variable is given to us, which we have to solve and find the value of y. 

So, let’s solve the above equation,

2y = 5y – (18/5)

(18/5) = 5y – 2y

(18/5) = 3y

y = (18/5) × (1/3)

y = (6/5) × (1/1)

y = 6/5

Hence, the value of y is 6/5.

Explanation:

Any value of the variable which makes both sides of an equation equal is known as a solution of the equation.

We know that, linear equation in one variable has only one variable term with the power 1.

So, the value which satisfy the equation is known as the solution of that equation.

Here, for I've variable we get only one solution.

Explanation:

9x – 3 = –21 has the solution (–2)

Here, in the above question, equation in one variable is given to us, which we have to solve and find the value of blank space.

So, let’s solve the above equation by assuming that the black space as y, the value of x is given to us, which is -2.

(9 × (-2)) – y = -21

-18 – y = -21

– y = -21 + 18

– y = – 3

Y = 3

So, the value we will put in the black space is 3.

Explanation:

Three consecutive numbers whose sum is 12 are 3, 4 and 5.

Here, in the above question, we have to find the three consecutive numbers which will give to us 12 after their addition.

So, let’s suppose that the numbers are x,(x+1),(x+2).

So, the addition will be

x+(x+1)+(x+2)=12

3x+3=12

3x=12-3

3x=9

X=3

Hence, the numbers are 3,4 and 5.

Explanation:

The share of A when Rs 25 is divided between A and B so that A gets Rs. 8 more than B is Rs 16.50.

Here, in the above question, we have to find out the share of A and B so that A get Rs. 8 more than B.

So, let's assume that B get x share than A will get x+1.

Now, total Rs. is 25.

x + (x + 8) = 25

x + x + 8 = 25

2x + 8 = 25

2x = 25 – 8

2x = 17

x = 17/2

x = 8.5

Hence, A gets 

=x + 8

= 8.5 + 8

= Rs 16.5

And B get 8.5

Explanation:

A term of an equation can be transposed to the other side by changing its sign.

Here, in the above question we have tell about the rule NSFW fir translation.

When we take any number from one side to another side, so if the numbers is in addition it will convert into subtraction. And the number which is in multiplication will get into division.

For example:- 3x + 8 = 0

Transposing 8 to RHS and it becomes -8

3x = -8

X = -8/3

Explanation:

On subtracting 8 from x, the result is 2. The value of x is 10.

Here, we need to write the given condition into the equation form.

In the question it is given that on subtracting 8 from x, the result is 2,

= x – 8 = 2

Not, take 8 grin the left hand side to right hand side.

X = 2 + 8

X = 10

Explanation:

(x/5) + 30 = 18 has the solution as -60.

Here, in the above question, equation in one variable is given to us, which we have to solve and find the value of x.

(x/5) = 18 – 30

(x/5) = -12

X = -12 × 5

X = -60

Hence, the value of x is -60.

Explanation:

When a number is divided by 8, the result is –3. The number is -24.

Here, we have to write the given condition into the equation form and than find the value of x.

So, let's suppose that the number is x.

So, according to condition, by dividing the number by 8 we get -3.

x/8 = -3

x = -3 × 8

x = -24

Hence, the value is x is -24.

Explanation:

9 is subtracted from the product of p and 4, the result is 11. The value of p is 5.

Here, we have to write the given condition into the equation form and than find the value of p.

So, according to the condition given in the question we have to subtract 9 from the product of p and 4 to get 11.

4p – 9 = 11

4p = 11 + 9

4p = 20

P = 20/4

P = 5

Hence, three value of P is 5.

Explanation:

If (2/5)x – 2 = 5 – (3/5)x, then x = 7

Here, in the above question, equation in one variable is given to us, which we have to solve and find the value of x.

So, let’s solve the above equation,

(2/5)x – 2 = 5 – (3/5)x

Now, in the above question, variables are given on both the side of equation. So, take all the variable on one side and numerical verified in another side.

(2/5)x + (3/5)x = 5 + 2

(2x + 3x)/5 = 7

5x = 7 × 5

X = 35/5

X = 7

Hence, the value is x is 7.

Explanation:

After 18 years, Swarnim will be 4 times as old as he is now. His present age is 6 years.

Here, we have to write the given condition into the equation form and than find the value of x.

So, let’s suppose that the present age of the Swarnim is x.

So, according to the condition given in the question, after 18 years from now the age of Swarnim will be 4 times as old of her is now.

X + 18 = 4x

X – 4x = -18

– 3x = -18

– 3x/3 = (-18/3)

X = 6

Hence, the present age of  swarnim’s is 6 years.

Explanation:

Convert the statement Adding 15 to 4 times x is 39 into an equation 4x + 15 = 39.

Here, we have to write the given condition into the equation form.

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

Now, we have to add 15 to the 4 times of x to get 39.

4x+15=39.

Explanation:

The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then the expression for the new denominator is x + 9.

Here, we have to write the given condition into the equation form and find the new expression for denominator.

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

Now, we can write denominator as = x + 10

Rational number = x/(x + 10)

In the question, it is given that we need to increase the numerator by 1 and decrease the denominator by 1.

So, the new rational number = Numerator + 1/ (denominator – 1)

= (x + 1)/(x + 10 – 1)

= (x + 1)/(x + 9)

Hence, the new denominator is x + 9.

Explanation:

The sum of two consecutive multiples of 10 is 210. The smaller multiple is 100.

Here, we have to write the given condition into the equation form and than find the value of smallest multiple.

So, let’s suppose that the Consecutive multiply of 10 are 10x and 10x+10.

Now, summation of this two consecutive multiples of 10 = 10x + 10x + 10 = 210

20x + 10 = 210

20x = 210 – 10

20x = 200

x = 200/20

x = 10

Hence, the two consecutive multiples of 10 are 10x = 10 × 10 = 100

10x + 10 = (10 × 10) + 10

= 110

Therefore, the smaller multiple of 10 is 100.

Explanation:

False.

Here, we have to write the given condition into the equation form.

So, let’s suppose that the age of boy three year age is x.

Now, the age of boy two year age will be x+1.

Explanation:

False.

Here, we have to write the given condition into the equation form and than find the value of x.

So, the present age of Shikha and Reemu is give as p and 4p.

So, the age of Reemu after 5 years  will be = (4p + 5)

Explanation:

False.

Here, we have to write the given condition into the equation form.

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

Now, unit place is given as x and the sum is 9, hence the ten’s place will be 9-x.

So, the number is

= 10 (9 – x) + x

= 90 – 10x + x

= 90 – 9x

Explanation:

True.

Here, we have to write the given condition into the equation form and than find the value of x.

So, in the question, it is given that the present age of Anju is y and the present age of mother is 60-y.

Now, the age of mother before 5 year will be

= 65 – y – 5

= (60 – y) years

Explanation:

False.

Here, we have to write the given condition into the equation form and than find the number of boys.

So, let’s suppose that the number girls is 5x and that number of boys is 5y.

In the question, it is given that the number is boys is 9 more than that of number of girls.

So, we can write

5x – 4x = 9

X = 9

Hence, the number of boys = 5x = 5 × 9 = 45 boys

Explanation:

True.

Here, we have to write the given condition into the equation form and than find the ages of A and B 5 years ago.

So, let’s suppose that the present age of A is x than the present age of B will be 90-x.

Now, we have to find the ages of A and B 5 years ago.

So, the age of A and B 5 years ago will be,

Age of A 5 years before = (x – 5) years

and B’s age = (90 – x – 5) = (85 – x) years.

Explanation:

False.

We know that, linear equations have only one answer, but it is not correct that they don't have save answers. 

They can have save answers also.

Explanation:

False.

Here, in the above question, we are given a equation and we need to solve this equation partially.

Now, when we transposing -3 from left hand side to right hand side it will become +3.

So, the equation will become

3x – 3 = 9

3x = 9 + 3

3x = 12

Explanation:

False.

Here, in the above question, we are given a equation and we need to solve this equation partially.

Now, when we transposing -x from right hand side to left hand side it will become +x.   

2x = 4 – x

2x + x = 4

3x = 4

X = 3/4

Explanation:

False.

Here, in the above question, we are given a equation and we need to solve this equation partially.

Now, when we transposing (15/8) from left hand side to right hand side it will become –(15/8).

(15/8) – 7x = 9

– 7x = 9 – (15/8)

Explanation:

False.

Here, in the above question, we are given a equation and we need to solve this equation partially.

Now, when we transposing +1 from left hand side to right hand side it will become -1.

(x/3) + 1 = (7/15)

(x/3) = (7/15) – 1

(x/3) = (7 – 15)/15

(x/3) = -8/15

Explanation:

True.

Here, in the above question, we have to compare both the equation.

Now, there are two equation, first is

6x = 18

Now, multiplying both side by 3, we get

6x × 3 = 18 × 3

18x = 54

Explanation:

False.

Here, in the above question, we have to solve the given equation and find the value of x 

Now, the equation give to us is

x/11 = 15

So, to find the value of x multiplying both side by 11, we get

(x/11) × 11 = 15 × 11

X = 165

Explanation:

False.

We know that, even numbers have the difference of two.

So, if the first number is x than the next even number should be (x+2).

Explanation:

False.

Here, in the above question condition is given as we have to form a equation and than find the value of second number.

So, the first number is x than the second number should be (x+1).

= x + (93 – x) = 93

X + 93 – x = 93

x – x = 93 -93

0 = 0

Explanation:

False.

Here, in the above question condition is given as we have to form a equation and than find the value of second number.

So, the first number of x than the second number should be (40-x)

Note, let’s us assume that (40 – x) > x

So, 40 – x + 8 = 3 (x + 8)

48 – x = 3x + 24

– x – 3x = 24 -48

– 4x = -24

X = -24 × (-1/4)

X = 6

Hence, the first number is = 6

Other number is = 40 – x

= 40 – 6

= 34

Note, the difference between numbers is = 34 – 6 = 28

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

((3x – 8)/2x) = 1

Now, 2x given on LHD is in division form, so take it on RHS than it will be in multiplication form.

(3x – 8) = 2x

Now, take all the variables on one side and all the numerical value on another side.

3x – 2x = 8

x = 8

Hence, the value of x we get by solving the given equation is 8.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

(5x/(2x – 1)) = 2

Now, (2x-1) given on LHD is in division form, so take it on RHS than it will be in multiplication form.

5x = 2 × (2x – 1)

5x = 4x – 2

Now, take all the variables on one side and all the numerical value on another side.

5x – 4x = -2

x = -2

Hence, the value of x we get by solving the given equation is -2.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

((2x – 3)/(4x + 5)) = (1/3)

Now, (4x+5) given on LHD is in division form, so take it on RHS than it will be in multiplication form.

3 × (2x – 3) = 1 × (4x + 5)

6x – 9 = 4x + 5

Now, take all the variables on one side and all the numerical value on another side.

6x – 4x = 5 + 9

2x = 14

x = 14/2

x = 7

Hence, the value of x we get by solving the given equation is 7.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

(8/x) = (5/(x – 1))

Now, x given on LHD is in division form, so take it on RHS than it will be in multiplication form and (x-1) given on RHD is in division form, so take it on LHS than it will be in multiplication form.

8 × (x – 1) = 5 × x

8x – 8 = 5x

Now, take all the variables on one side and all the numerical value on another side.

8x – 5x = 8

3x = 8

X = 8/3

Hence, the value of x we get by solving the given equation is 8/3.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

[(5(1 – x)) + (3(1 + x))/ (1 – 2x)] = 8

Now, (1-2x) given on LHD is in division form, so take it on RHS than it will be in multiplication.

(5(1 – x)) + (3(1 + x)) = 8 × (1 – 2x)

5 – 5x + 3 + 3x = 8 – 16 x

8 – 2x = 8 – 16x

Now, take all the variables on one side and all the numerical value on another side.

16x – 2x = 8 – 8

14x = 0

x = 0/14

x = 0

Hence, the value of x we get by solving the given equation is 0.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

((0.2x + 5)/ (3.5x – 3)) = (2/5)

Now, (3.5x-3) given on LHD is in division form, so take it on RHS than it will be in multiplication.

5 × (0.2x + 5) = 2 × (3.5x – 3)

x + 25 = 7x – 6

Now, take all the variables on one side and all the numerical value on another side.

25 + 6 = 7x – x

31 = 6x

x = 31/6

Hence, the value of x we get by solving the given equation is 31/6.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of y.

So, the equation given to us is

[(y – (4 – 3y))/ (2y – (3 + 4y))] = 1/5

(y – 4 + 3y)/ (2y – 3 – 4y) = 1/5

(-4y – 4)/ (2y – 3) = 1/5

Now, (2y-3) given on LHD is in division form, so take it on RHS than it will be in multiplication.

5 × (-4y – 4) = 1 × (2y – 3)

20y – 20 = 2y – 3

Now, take all the variables on one side and all the numerical value on another side.

20y – 2y = 20 – 3

22 y = 17

y = 17/22

Hence, the value of y we get by solving the given equation is 17/22.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

(x/5) = (x – 1)/6

Now, (x-1) given on LHD is in division form, so take it on RHS than it will be in multiplication.

6 × x = 5 × (x – 1)

6x = 5x – 5

Now, take all the variables on one side and all the numerical value on another side.

6x – 5x = -5

x = -5

Hence, the value of x we get by solving the given equation is -5.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

0.4(3x –1) = 0.5x + 1

1.2x – 0.4 = 0.5x + 1

Now, take all the variables on one side and all the numerical value on another side.

1.2x – 0.5x = 1 + 0.4

0.7x = 1.4

x = 1.4/0.7

x = 14/7

x = 2

Hence, the value of x we get by solving the given equation is 2.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

8x – 7 – 3x = 6x – 2x – 3

5x – 7 = 4x – 3

Now, take all the variables on one side and all the numerical value on another side.

5x – 4x = 7 – 3

x = 4

Hence, the value of x we get by solving the given equation is 4.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

10x – 5 – 7x = 5x + 15 – 8

3x – 5 = 5x + 7

Now, take all the variables on one side and all the numerical value on another side.

3x – 5x = 7 + 5

– 2x = 12

x = -12/2

x = – 6

Hence, the value of x we get by solving the given equation is -6.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of t.

So, the equation given to us is

4t – 3 – (3t +1) = 5t – 4

4t – 3 – 3t – 1 = 5t – 4

t – 4 = 5t – 4

Now, take all the variables on one side and all the numerical value on another side.

4 – 4 = 5t – t

0 = 4t

t = 0/4

t = 0

Hence, the value of t we get by solving the given equation is 0.

Explanation:

Here, in the above question, we are given as equation and we have to solve that equation to find the value of x.

So, the equation given to us is

5(x – 1) – 2(x + 8) = 0

5x – 5 – 2x – 16 = 0

3x – 21 = 0

Now, take all the variables on one side and all the numerical value on another side.

3x = 21

x = 21/3

x = 7

Hence, the value of x we get by solving the given equation is 7.