Answer
x = 1
OR
x = 3
Step-by-step explanation
We are asked to solve the absolute value equation
|2x - 4| + 6 = 8
Subtract 6 from both sides
|2x - 4| + 6 - 6 = 8 - 6
|2x - 4| = 2
To solve an expression with the absolute value symbol. we obtain two solutions for it.
We first solve when the other side of the equation to the absolute value symbol has positive sign.
Then, we obtain another solution by setting that other side (the right-hand side) to negative.
So, the first solution,
2x - 4 = 2
Add 4 to both sides
2x - 4 + 4 = 2 + 4
2x = 6
Divide both sides by 2
(2x/2) = (6/2)
x = 3
Second solution,
2x - 4 = -2
Add 4 to both sides
2x - 4 + 4 = -2 + 4
2x = 2
Divide both sides by 2
(2x/2) = (2/2)
x = 1
Hope this Helps!!!