# Equations with variables on both sides

## Grade 8 Math Worksheets

**Let us see the example below:**

**8 x = 5x + 9**

Subtracting 5*x* from both sides,

8*x* – 5*x *= 5*x *+ 9 – 5*x*

3*x *= 9

Divide by ‘3’ on both sides, we get *x* = 3

*Example**: *Solve for *x*, if 5*x* + 4 = 18 + 3*x*

Subtract 3*x* and 4 from both sides, 5*x* + 4 = 18 + 3*x*

5*x* + 4 – 3*x* – 4 = 18 + 3*x *– 3*x* – 4

2*x* = 14

Divide by ‘2’ on both sides, we get *x* = 7

**Check your answer: **Put *x* = 7 in 5*x* + 4 = 18 + 3*x*

L.H.S = (5 × 7) + 4 = 35 + 4 = 39

R.H.S = 18 + (3 × 7) = 18 + 21 = 39

Since L.H.S = R.H.S, so *x* = 7 is the answer.

**Check Point**

- Solve for
*x*: 2*x*+ 9 = 5*x* - Solve for
*y*: 3*y*+ 1 = 4*y*+ 12 - Solve for
*x*: 3*x*+ 3 = 4*x*– 8 - Solve for
*y*: 2*y*– 10 = 7*y* - Solve for
*z*: 20 –*z*= 16 – 5*z*

##### Answer key

- 3
- -11
- 11
- -2
- -1

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