)(b)(c)(d)x|x + 8| − 9 < 10

To solve the inequality |x| + |x + 8| - 9 < 10, we need to consider different cases because of the absolute value signs.

Case 1: x >= 0 and x + 8 >= 0 This means x is in the interval [0, ∞). The inequality becomes: x + x + 8 - 9 < 10 2x - 1 < 10 2x < 11 x < 5.5

Case 2: x >= 0 and x + 8 < 0 This means x is in the interval [0, -8). But this is impossible because x cannot be both non-negative and negative.

Case 3: x < 0 and x + 8 >= 0 This means x is in the interval (-∞, 0). The inequality becomes: -x + x + 8 - 9 < 10 -x < 11 x > -11

Case 4: x < 0 and x + 8 < 0 This means x is in the interval (-∞, -8). The inequality becomes: -x - (x + 8) - 9 < 10 -2x - 17 < 10 -2x < 27 x > -13.5

Combining all these cases, the solution to the inequality is x in (-∞, 5.5).