Grade 8 Linear Equations: Variables on Both Sides

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Solve: 7x − 8 = 4x − 29

   1. Subtract 4x from both sides: 3x − 8 = −29.
   2. Add 8 to both sides: 3x = −29 + 8 = −21.
   3. Divide both sides by 3: x = −21 ÷ 3 = −7.
   4. Check: 7 × (−7) − 8 = −57 and 4 × (−7) − 29 = −57 ✓ So x = −7.

   Answer: −7

2. Example 2

   Solve: 3(x + 4) = 2x + 14

   1. Distribute the 3: 3(x + 4) = 3x + 12, so 3x + 12 = 2x + 14.
   2. Subtract 2x from both sides: x + 12 = 14.
   3. Subtract 12 from both sides: x = 14 − 12 = 2.
   4. Check: 3 × (2 + 4) = 18 and 2 × 2 + 14 = 18 ✓ So x = 2.

   Answer: 2

3. Example 3

   Solve: 5(x − 4) = 3(x − 4)

   1. On the left: Distribute the 5: 5(x − 4) = 5x − 20.
   2. On the right: Distribute the 3: 3(x − 4) = 3x − 12, so 5x − 20 = 3x − 12.
   3. Subtract 3x from both sides: 2x − 20 = −12.
   4. Add 20 to both sides: 2x = −12 + 20 = 8.
   5. Divide both sides by 2: x = 8 ÷ 2 = 4.
   6. Check: 5 × (4 − 4) = 0 and 3 × (4 − 4) = 0 ✓ So x = 4.

   Answer: 4