Grade 7 Equations: Multi-Step Equations

Worked examples

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

1. Example 1

   Solve: 6(x + 9) = 120

   1. Distribute the 6: 6 × x + 6 × 9 = 6x + 54, so 6x + 54 = 120.
   2. Subtract 54 from both sides: 6x = 120 − 54 = 66.
   3. Divide both sides by 6: x = 66 ÷ 6 = 11.
   4. Check: 6 × (11 + 9) = 120 ✓ So x = 11.

   Answer: 11

2. Example 2

   Solve: 7(x + 4) = 98

   1. Distribute the 7: 7 × x + 7 × 4 = 7x + 28, so 7x + 28 = 98.
   2. Subtract 28 from both sides: 7x = 98 − 28 = 70.
   3. Divide both sides by 7: x = 70 ÷ 7 = 10.
   4. Check: 7 × (10 + 4) = 98 ✓ So x = 10.

   Answer: 10

3. Example 3

   Solve: 5(x + 13) = −10

   1. Distribute the 5: 5 × x + 5 × 13 = 5x + 65, so 5x + 65 = −10.
   2. Subtract 65 from both sides: 5x = −10 − 65 = −75.
   3. Divide both sides by 5: x = −75 ÷ 5 = −15.
   4. Check: 5 × (−15 + 13) = −10 ✓ So x = −15.

   Answer: −15