Question

Solve the equation shown below. Explain each step you took and show your work. *You need to show all steps*
*Hint: remember to set up two equations
2 |2x + 4 | = 12

Answer 1

We solve 2 |2x + 4| = 12.

1. Isolate the absolute value by dividing both sides by 2:
|2x + 4| = 12 ÷ 2 = 6

2. An absolute value equation |A| = 6 gives two cases: A = 6 or A = −6. Here A = 2x + 4.
Case 1: 2x + 4 = 6
Case 2: 2x + 4 = −6

3. Solve each case.
Case 1: 2x + 4 = 6
2x = 6 − 4 = 2
x = 2 ÷ 2 = 1

Case 2: 2x + 4 = −6
2x = −6 − 4 = −10
x = −10 ÷ 2 = −5

4. Check both solutions in the original equation:
For x = 1: 2|2(1) + 4| = 2|2 + 4| = 2|6| = 2·6 = 12 ✓
For x = −5: 2|2(−5) + 4| = 2|−10 + 4| = 2|−6| = 2·6 = 12 ✓

Solutions: x = 1 or x = −5.