Question

What is the solution to –4|–2x + 6| = –24?x = 0x = 0 or x = –6x = 0 or x = 6no solution

Answer 1

Note that –4|–2x + 6| = –24 can be greatly simplified by dividing both sides by -4: |-2x+6| = 6. This, in turn, can be simplified by dividing everything by 2:

|-x+3| = 3. There are two solutions:

Case 1: -x+3 is already positive. The absolute value operator is unneeded. -x+3 = 3. Then x = 0.

Case 2: -x+3 is negative. Then rewrite |-x+3| = 3 as -(-x+3) = 3. Solving for x: x - 3 = 3, and x = 6.

The solution set is {0, 6}.

Answer 2

The correct answers are the x = 6 and x = 0.

In order to find this, we can follow the order of operations.

–4|–2x + 6| = –24

Divide by -4

|–2x + 6| = 6

Since it is now equal to a absolute value, we have to solve for the positive and negative versions of the final answer. Let's start with the positive.

-2x + 6 = 6

-2x = 0

x = 0

Now for the negative

-2x - 6 = -6

-2x = -12

x = 6

These would be your two answers.