Question

solve the equation. check your answers. 2|2x - 1| = 18 x = \square (type an integer or a simplified fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Isolate the absolute value

Divide both sides by 2:
$\frac{2|2x-1|}{2} = \frac{18}{2}$
$|2x-1| = 9$

Step2: Split into two linear equations

For absolute value $|A|=B$, solve $A=B$ and $A=-B$:
$2x-1 = 9$ and $2x-1 = -9$

Step3: Solve first linear equation

Add 1, then divide by 2:
$2x = 9+1$
$2x = 10$
$x = \frac{10}{2} = 5$

Step4: Solve second linear equation

Add 1, then divide by 2:
$2x = -9+1$
$2x = -8$
$x = \frac{-8}{2} = -4$

Step5: Verify solutions

For $x=5$: $2|2(5)-1|=2|9|=18$, which matches.
For $x=-4$: $2|2(-4)-1|=2|-9|=18$, which matches.

Answer:

$5, -4$