Grade 8 Linear Equations: Unit Review

Worked examples

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

1. Example 1

   Solve: 7(x + 1) = 63

   1. Distribute the 7: 7 × x + 7 × 1 = 7x + 7, so 7x + 7 = 63.
   2. Subtract 7 from both sides: 7x = 63 − 7 = 56.
   3. Divide both sides by 7: x = 56 ÷ 7 = 8.
   4. Check: 7 × (8 + 1) = 63 ✓ So x = 8.

   Answer: 8

2. Example 2

   Solve: 4(x + 11) = −12

   1. Distribute the 4: 4 × x + 4 × 11 = 4x + 44, so 4x + 44 = −12.
   2. Subtract 44 from both sides: 4x = −12 − 44 = −56.
   3. Divide both sides by 4: x = −56 ÷ 4 = −14.
   4. Check: 4 × (−14 + 11) = −12 ✓ So x = −14.

   Answer: −14

3. Example 3

   Solve: 4(x + 13) = 108

   1. Distribute the 4: 4 × x + 4 × 13 = 4x + 52, so 4x + 52 = 108.
   2. Subtract 52 from both sides: 4x = 108 − 52 = 56.
   3. Divide both sides by 4: x = 56 ÷ 4 = 14.
   4. Check: 4 × (14 + 13) = 108 ✓ So x = 14.

   Answer: 14