Question

what are the solutions for the absolute value equation $-72|x - 2| = -720$? (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

Divide both sides by $-72$:
$$\frac{-72|x-2|}{-72} = \frac{-720}{-72}$$
Simplify to get $|x-2| = 10$

Step2: Split into two equations

Absolute value rule: $|A|=B \Rightarrow A=B$ or $A=-B$:
$x-2 = 10$ or $x-2 = -10$

Step3: Solve first equation

Add 2 to both sides:
$x = 10 + 2 = 12$

Step4: Solve second equation

Add 2 to both sides:
$x = -10 + 2 = -8$

Step5: Order solutions

Arrange from smallest to largest: $x=-8$, $x=12$

Answer:

$x = -8$ or $x = 12$