Question

Solve for x: −3|2x + 6| = −12

A.) x = 1 and x = 5
B.) x = −1 and x = −5
C.) x = −9 and x = 3
D.) No solution

Answer 1

`-3|2x + 6| = -12 \\ |2x+6|=4\\ 2|x+3|=4\\ |x+3|=2\\ x+3 =-2 \vee x+3=2\\ x=-5 \vee x=-1`

Answer 2

Since this is an equation involving an absolute value, let 2x + 6 be positive first such that,

-3(2x + 6) = -12
2x + 6 = 4
2x = -2, x = -1
Then, let 2x + 6 be negative,
-3(-2x - 6) = -12
-2x - 6 = 4
-2x = 10 ; x = -5
Thus, the answer to this item is letter B.