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

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:
\[
|x+10| = \frac{48}{4}
\]
\[
|x+10| = 12
\]

Now we have the absolute value equation. This gives us two cases to solve:

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

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

Thus, the solutions to the equation \(4|x+10| - 12 = 36\) are \(x = 2\) and \(x = -22\).

The correct response is:
\[
x = 2, -22
\]