Chapter 4: Linear Equations in One Variable

Solution:-

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

3 + 4 + 5 = 12

Solution:-

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.

Let us assume B share be x

As per the condition in the question, A share be x + 8

Then,

x + (x + 8) = 25

x + x + 8 = 25

2x + 8 = 25

2x = 25 – 8

2x = 17

x = 17/2

x = 8.5

So, A gets x + 8

= 8.5 + 8

= Rs 16.5

Solution:-

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

For example:- 2x + 3 = 0

Transposing 3 to RHS and it becomes -3

2x = -3

X = -3/2

Solution:-

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

From the question,

On subtracting 8 from x, the result is 2,

= x – 8 = 2

Transposing -8 to RHS and it becomes 8

X = 2 + 8

X = 10

Solution:-

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

Given, (x/5) + 30 = 18

Transposing 30 to RHS and it becomes -30.

(x/5) = 18 – 30

(x/5) = -12

X = -12 × 5

X = -60

Solution:-

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

Let the number be x,

Then,

x/8 = -3

x = -3 × 8

x = -24

Solution:-

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

From the question, it is given that,

9 is subtracted from the product of p and 4, the result is 11 = 4p – 9 = 11

4p – 9 = 11

Transposing -9 to RHS and it becomes 9.

4p = 11 + 9

4p = 20

P = 20/4

P = 5

Solution:-

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

Given,

(2/5)x – 2 = 5 – (3/5)x

Transposing -2 to RHS and it becomes 2 and (3/5)x to LHS it becomes –(3/5)x.

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

(2x + 3x)/5 = 7

5x = 7 × 5

X = 35/5

X = 7

Solution:-

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

Let us assume swarnim’s parent age be x years.

Then, after 18 years, Swarnim’s age = (x + 18) year

According to the question,

X + 18 = 4x

X – 4x = -18

– 3x = -18

– 3x/3 = (-18/3)

X = 6

Therefore, swarnim’s present age is 6 years.

Solution:-

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