Question

solve for all values of $x$ in simplest form.
$2|9 - 2x| - 9 = 1$

Explanation:

Step1: Isolate the absolute - value term

Add 9 to both sides of the equation $2|9 - 2x|-9 = 1$.
$2|9 - 2x|=1 + 9$
$2|9 - 2x|=10$
Then divide both sides by 2: $|9 - 2x| = 5$.

Step2: Set up two equations

Since $|a|=b$ ($b\geq0$) implies $a = b$ or $a=-b$, we have two equations:
Equation 1: $9 - 2x=5$.
Subtract 9 from both sides: $-2x=5 - 9=-4$.
Divide both sides by -2: $x = 2$.
Equation 2: $9 - 2x=-5$.
Subtract 9 from both sides: $-2x=-5 - 9=-14$.
Divide both sides by -2: $x = 7$.

Answer:

$x = 2$ or $x = 7$