Grade 7 Equations: With Distributive Property

Worked examples

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

1. Example 1

   Solve: 5(x − 3) = −25

   1. Distribute the 5: 5 × x + 5 × (−3) = 5x − 15, so 5x − 15 = −25.
   2. Add 15 to both sides: 5x = −25 + 15 = −10.
   3. Divide both sides by 5: x = −10 ÷ 5 = −2.
   4. Check: 5 × (−2 − 3) = −25 ✓ So x = −2.

   Answer: −2

2. Example 2

   Solve: 8(x + 9) = 120

   1. Distribute the 8: 8 × x + 8 × 9 = 8x + 72, so 8x + 72 = 120.
   2. Subtract 72 from both sides: 8x = 120 − 72 = 48.
   3. Divide both sides by 8: x = 48 ÷ 8 = 6.
   4. Check: 8 × (6 + 9) = 120 ✓ So x = 6.

   Answer: 6

3. Example 3

   Solve: 6(x + 1) − 10 = 50

   1. Distribute the 6: 6(x + 1) = 6x + 6.
   2. Combine like terms: 6x + 6 − 10 = 6x − 4, so 6x − 4 = 50.
   3. Add 4 to both sides: 6x = 50 + 4 = 54.
   4. Divide both sides by 6: x = 54 ÷ 6 = 9.
   5. Check: 6 × (9 + 1) − 10 = 50 ✓ So x = 9.

   Answer: 9