Equations with variables on both sides

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We can see some equations where variable (the unknown quantity) appears on both sides of an equation. We can solve such equations in the same way as we solve equations with numerical values on both sides.

Let us see the example below:

8x = 5x + 9

Subtracting 5x from both sides,

8x – 5x = 5x + 9 – 5x

3x = 9

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

equations with variables on both sides

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

 

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

 

5x + 4 – 3x – 4 = 18 + 3x – 3x – 4

 

2x = 14

 

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

 

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

 

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

 

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

 

Answer key
  1. 3
  2. -11
  3. 11
  4. -2
  5. -1