Question

question
solve for all values of x in simplest form.
-3|2 + 2x| - 3 = -36
answer attempt 1 out of 2
+ additional solution - no solution
x =

Explanation:

Step1: Isolate the absolute value term

Add 3 to both sides of the equation:
$-3|2 + 2x| - 3 + 3 = -36 + 3$
Simplify to get:
$-3|2 + 2x| = -33$

Step2: Divide by -3

Divide both sides by -3:
$\frac{-3|2 + 2x|}{-3} = \frac{-33}{-3}$
Simplify to get:
$|2 + 2x| = 11$

Step3: Solve the absolute value equation

The absolute value equation $|A| = B$ (where $B \geq 0$) has solutions $A = B$ or $A = -B$. So we have two cases:

Case 1: $2 + 2x = 11$

Subtract 2 from both sides:
$2 + 2x - 2 = 11 - 2$
Simplify:
$2x = 9$
Divide by 2:
$x = \frac{9}{2}$

Case 2: $2 + 2x = -11$

Subtract 2 from both sides:
$2 + 2x - 2 = -11 - 2$
Simplify:
$2x = -13$
Divide by 2:
$x = -\frac{13}{2}$

Answer:

$x = \frac{9}{2}$ or $x = -\frac{13}{2}$