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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

1 answer

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: \[ x = 2, -22 \]