What is the solution set for |x+3| = 6?

To find the solution set for |x+3| = 6, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: x+3 is positive: In this case, we can remove the absolute value signs and solve for x: x+3 = 6 Subtracting 3 from both sides, we get: x = 3

Case 2: x+3 is negative: In this case, we need to negate the expression inside the absolute value signs and solve for x: -(x+3) = 6 Distributing the negative sign, we get: -x - 3 = 6 Adding 3 to both sides, we get: -x = 9 Multiplying both sides by -1 to isolate x, we get: x = -9

Therefore, the solution set for |x+3| = 6 is {3, -9}.