Question

9(3x − 16) + 15 = 6x − 24

Part A: Show or explain the calculations you use to solve the equation.

Answer 1

Start by using the distributive property, then combine like terms and isolate x.

1. Expand: 9(3x − 16) + 15 = 6x − 24
→ 27x − 144 + 15 = 6x − 24

2. Combine like terms on the left: −144 + 15 = −129
→ 27x − 129 = 6x − 24

3. Subtract 6x from both sides to collect x-terms: 27x − 6x − 129 = −24
→ 21x − 129 = −24

4. Add 129 to both sides to isolate the x-term: 21x = 105

5. Divide both sides by 21: x = 105 / 21 = 5

Check: Left side = 9(3·5 − 16) + 15 = 9(15 − 16) + 15 = 9(−1) + 15 = 6
Right side = 6·5 − 24 = 30 − 24 = 6

Both sides equal, so x = 5 is correct.