Question

|3x+7|= -15 2. |b+5|=2b-9

Answer 1

1. The absolute value function takes any quantity and makes it positive, so it's impossible to have |3x + 7| < 0. There is no solution.

2. If b + 5 ≥ 0, then

|b + 5| = b + 5 = 2b - 9

b = 14

Otherwise, if b + 5 < 0, then

|b + 5| = -(b + 5) = 2b - 9

-b - 5 = 2b - 9

3b = -4

b = -4/3

However, this second solution is extraneous, since the left side is positive,

|-4/3 + 5| > 0

while the right side is negative,

2•(-4/3) - 9 = -8/3 - 9 < 0