solve the absolute value equation

3{2x-2} + 8 = 20

Help (with baby steps please)
I know answer is x=-1 or x=3
( I get the 3 but not the -1)
thank you again

Distribute the 3:

6x - 6 + 8 = 20

Subtract 8-6:
6x + 2 = 20

Subtract 2:
6x = 20 -2

6x = 18

Divide 6 on both sides:

(6x/6) = 18/6

x = 3

(x = -1 is not an answer)

3|2x-2| + 8 = 20

3|2x-2| = 12
|2x-2| = 4
2x - 2 = 4 OR 2x-2 = -4
2x = 6 OR 2x = -2
x = 3 OR x = -1

both answers are valid

3|2x-2| + 8 = 20

3|2x-2| = 12
|2x-2| = 4
|x-1| = 2
x-1 = ±2
x = 1±2
x = 3 or -1

To solve the absolute value equation 3|2x - 2| + 8 = 20, we can follow these steps:

Step 1: Isolate the absolute value on one side of the equation.
To do this, let's start by subtracting 8 from both sides of the equation:
3|2x - 2| = 12

Step 2: Divide both sides of the equation by 3 to eliminate the coefficient of the absolute value.
(3|2x - 2|) / 3 = 12 / 3
|2x - 2| = 4

Step 3: Split the absolute value equation into two separate equations.
We need to consider the positive and negative cases of the absolute value separately. So, we'll write two equations, one with the positive value and one with the negative value of the absolute value expression.
Equation 1: 2x - 2 = 4 (positive case)
Equation 2: -(2x - 2) = 4 (negative case)

Step 4: Solve each equation separately.

For Equation 1:
2x - 2 = 4
Add 2 to both sides:
2x = 4 + 2
2x = 6
Divide both sides by 2:
x = 6 / 2
x = 3

For Equation 2:
-(2x - 2) = 4
Distribute the negative sign:
-2x + 2 = 4
Subtract 2 from both sides:
-2x = 4 - 2
-2x = 2
Divide both sides by -2 (note that dividing by a negative value flips the inequality):
x = 2 / -2
x = -1

So the solutions to the absolute value equation 3|2x - 2| + 8 = 20 are x = 3 and x = -1.