Question

What is the solution to –4|–2x + 6| = –24?

Answer 1

x=0 or x=6

Explanation:

Step 1: Divide both sides by -4.

−4(|−2x+6|)

−4

=

−24

−4

|−2x+6|=6

Step 2: Solve Absolute Value.

|−2x+6|=6

We know either−2x+6=6or−2x+6=−6

−2x+6=6(Possibility 1)

−2x+6−6=6−6(Subtract 6 from both sides)

−2x=0

−2x

−2

=

0

−2

(Divide both sides by -2)

x=0

−2x+6=−6(Possibility 2)

−2x+6−6=−6−6(Subtract 6 from both sides)

−2x=−12

−2x

−2

=

−12

−2

(Divide both sides by -2)

x=6

Answer 2

x = 0 or x = 6

Explanation:

–4|–2x + 6| = –24

Divide both sides by -4.

|–2x + 6| = 6

Set the inside of the absolute value equal to 6 and -6.

-2x + 6 = 6 or -2x + 6 = -6

-2x = 0 or -2x = -12

x = 0 or x = 6