Final answer:
To solve the equation -24 = |x-15|, consider two cases: when x-15 is positive and when it is negative. The solutions are x = 39 and x = -9.
Step-by-step explanation:
To solve the equation -24 = |x-15|, we need to consider two cases: when x-15 is positive and when it is negative.
Case 1: x-15 < 0
If x-15 is negative, we can rewrite the equation as -24 = -(x-15). Simplifying, we get -24 = -x + 15. To isolate x, we subtract 15 from both sides and then multiply by -1, giving x = 39.
Case 2: x-15 ≥ 0
If x-15 is non-negative, we can rewrite the equation as -24 = x-15. Simplifying, we get -9 = x. Therefore, the two possible solutions are x = 39 and x = -9.