Question

Solve for x: -2|4x + 12| = -32 (5 points)

no solution
x = 1, x = -1
x = 1x = -7
x = -1, x = 7​

Answer 1

x = 1, x = -7

Explanation:

Step 1: Divide both sides by -2.

• 
  `(-2(|4x+12|))/(-2) = (-32)/(-2)`
• 
  `|4x + 12| = 16`

Step 2: Solve absolute value.

• We know either 4x + 12 = 16 or 4x + 12 = -16.

1st Possibility:

• 4x + 12 = 16
• 4x + 12 - 12 = 16 - 12 (Subtract 12 from both sides)
• 4x = 4
• 4x/4 = 4/4 (Divide both sides by 4)
• x = 1

2nd possibility:

• 4x + 12 = -16
• 4x + 12 - 12 = -16 - 12 (Subtract 12 from both sides)
• 4x = -28
• 4x/4 = -28/4 (Divide both sides by 4)
• x = -7

Therefore, the answer is x = 1, x = -7.