Question

question 4
what are the solutions for the absolute value equation $-4|x - 3| + 8 = -80$?
(fill each blank with an integer where the smaller integer is on the first blank)
$x = \square$ or $x = \square$

Explanation:

Step1: Isolate absolute value term

Subtract 8 from both sides:
$-4|x - 3| = -80 - 8$
$-4|x - 3| = -88$

Step2: Solve for absolute value

Divide by -4 on both sides:
$|x - 3| = \frac{-88}{-4}$
$|x - 3| = 22$

Step3: Split into two equations

Set up positive and negative cases:
$x - 3 = 22$ or $x - 3 = -22$

Step4: Solve first equation

Add 3 to both sides:
$x = 22 + 3$
$x = 23$

Step5: Solve second equation

Add 3 to both sides:
$x = -22 + 3$
$x = -17$

Step6: Order solutions

Arrange from smallest to largest:
$x = -17$ or $x = 23$

Answer:

$x = -17$ or $x = 23$