Question

Solve the following absolute value equation:

4|x+10|−12=36


(1 point)
Responses

x=36, −12
x=36, −12

x=4, −10
x=4, −10

x=2, −22
x=2, −22

x=22, −2
x=22, −2

Answer 1

To solve the equation \( 4|x+10|−12=36 \), we first isolate the absolute value term.

1. Add 12 to both sides:
\[
4|x + 10| = 36 + 12
\]
\[
4|x + 10| = 48
\]

2. Divide both sides by 4:
\[
|x + 10| = \frac{48}{4}
\]
\[
|x + 10| = 12
\]

3. Now we can set up two cases based on the property of absolute value.

**Case 1:**
\[
x + 10 = 12
\]
Subtract 10 from both sides:
\[
x = 12 - 10
\]
\[
x = 2
\]

**Case 2:**
\[
x + 10 = -12
\]
Subtract 10 from both sides:
\[
x = -12 - 10
\]
\[
x = -22
\]

Thus, the solutions to the equation are:
\[
x = 2 \quad \text{and} \quad x = -22
\]

The correct response is:
**x=2, −22**.