Grade 8 Linear Equations: Multi-Step Equations

Worked examples

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

1. Example 1

   Solve: 7(x + 13) = 70

   1. Distribute the 7: 7 × x + 7 × 13 = 7x + 91, so 7x + 91 = 70.
   2. Subtract 91 from both sides: 7x = 70 − 91 = −21.
   3. Divide both sides by 7: x = −21 ÷ 7 = −3.
   4. Check: 7 × (−3 + 13) = 70 ✓ So x = −3.

   Answer: −3

2. Example 2

   Solve: 5(x + 1) = 70

   1. Distribute the 5: 5 × x + 5 × 1 = 5x + 5, so 5x + 5 = 70.
   2. Subtract 5 from both sides: 5x = 70 − 5 = 65.
   3. Divide both sides by 5: x = 65 ÷ 5 = 13.
   4. Check: 5 × (13 + 1) = 70 ✓ So x = 13.

   Answer: 13

3. Example 3

   Solve: 7(x + 13) = 112

   1. Distribute the 7: 7 × x + 7 × 13 = 7x + 91, so 7x + 91 = 112.
   2. Subtract 91 from both sides: 7x = 112 − 91 = 21.
   3. Divide both sides by 7: x = 21 ÷ 7 = 3.
   4. Check: 7 × (3 + 13) = 112 ✓ So x = 3.

   Answer: 3