Algebra-1

To solve the inequality 9 |x + 8| + 10 < 55, we can begin by subtracting 10 from both sides:

9 |x + 8| < 45

Next, we can divide both sides by 9. However, we need to consider two cases based on the sign of (x + 8):

Case 1: x + 8 is nonnegative (i.e., x + 8 ≥ 0)
In this case, the absolute value |x + 8| is equal to x + 8, so we have:
9(x + 8) < 45

Solving this inequality, we get:
9x + 72 < 45
9x < 45 - 72
9x < -27
x < -3

Case 2: x + 8 is negative (i.e., x + 8 < 0)
In this case, the absolute value |x + 8| is equal to -(x + 8...