Question

solve $|x - 2| + 5 = 9$.
the solutions are $x = \square$ and $x = \square$.

Explanation:

Step1: Isolate the absolute value

Subtract 5 from both sides.
$|x-2| + 5 - 5 = 9 - 5$
$|x-2| = 4$

Step2: Split into two cases

For absolute value equations, $|A|=B$ means $A=B$ or $A=-B$.
Case 1: $x-2 = 4$
Case 2: $x-2 = -4$

Step3: Solve Case 1

Add 2 to both sides.
$x = 4 + 2$
$x = 6$

Step4: Solve Case 2

Add 2 to both sides.
$x = -4 + 2$
$x = -2$

Answer:

$x = 6$ and $x = -2$