Question

question
solve for all values of ( x ) in simplest form.
( |2 - 2x| + 1 = 7 )

Explanation:

Step1: Isolate the absolute value

Subtract 1 from both sides.
$|2-2x| = 7 - 1$
$|2-2x| = 6$

Step2: Split into two cases

Case 1: Inside absolute value is non-negative.
$2-2x = 6$
Case 2: Inside absolute value is negative.
$2-2x = -6$

Step3: Solve Case 1

Isolate $x$ by rearranging terms.
$-2x = 6 - 2$
$-2x = 4$
$x = \frac{4}{-2} = -2$

Step4: Solve Case 2

Isolate $x$ by rearranging terms.
$-2x = -6 - 2$
$-2x = -8$
$x = \frac{-8}{-2} = 4$

Answer:

$x=-2$ and $x=4$