Question

question 4
what are the solutions for the absolute value equation $-4|x - 2| + 8 = -80$?
(fill each blank with an integer where the smaller integer is on the first blank.)
$x = \square$ or $x = \square$

Explanation:

Step1: Isolate the absolute value term

Subtract 8 from both sides:
$-4|x-2| = -80 - 8$
$-4|x-2| = -88$

Step2: Solve for $|x-2|$

Divide both sides by -4:
$|x-2| = \frac{-88}{-4}$
$|x-2| = 22$

Step3: Set up two linear equations

For absolute value equality, split into two cases:
$x-2 = 22$ or $x-2 = -22$

Step4: Solve first linear equation

Add 2 to both sides:
$x = 22 + 2$
$x = 24$

Step5: Solve second linear equation

Add 2 to both sides:
$x = -22 + 2$
$x = -20$

Step6: Order the solutions

Sort the results from smallest to largest:
$x=-20$ or $x=24$

Answer:

$x=-19$ or $x=23$