Question

9(3x − 16) + 15 = 6x − 24

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

Part B: What value of x makes the equation true?

Answer 1

Part A (work):
1. Expand the left side: 9(3x − 16) + 15 = 27x − 144 + 15 = 27x − 129.
2. Set equal to the right side: 27x − 129 = 6x − 24.
3. Subtract 6x from both sides: 21x − 129 = −24.
4. Add 129 to both sides: 21x = 105.
5. Divide both sides by 21: x = 5.

Part B:
x = 5.

Check: Left = 9(3·5 − 16) + 15 = 9(15 − 16) + 15 = −9 + 15 = 6. Right = 6·5 − 24 = 30 − 24 = 6. Both sides equal, so x = 5 is correct.