|2r-2|=12

Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.

2r-2=±12

Set up the positive portion of the ± solution.

2r-2=12

Move all terms not containing r to the right side of the equation.

Add 2 to both sides of the equation.

2r=12+2

Add 12 and 2.

2r=14

2r=14

Divide each term by 2 and simplify.

Divide each term in 2r=14 by 2.

2r2=142

Cancel the common factor of 2.

Cancel the common factor.

2r2=142

Divide r by 1.

r=142

r=142

Divide 14 by 2.

r=7

r=7

r=7

Set up the negative portion of the ± solution.

2r-2=-12

Move all terms not containing r to the right side of the equation.

Add 2 to both sides of the equation.

2r=-12+2

Add -12 and 2.

2r=-10

2r=-10

Divide each term by 2 and simplify.

Divide each term in 2r=-10 by 2.

2r2=-102

Cancel the common factor of 2.

Cancel the common factor.

2r2=-102

Divide r by 1.

r=-102

r=-102

Divide -10 by 2.

r=-5

r=-5

r=-5

The solution to the equation includes both the positive and negative portions of the solution.

r=7,-5

Solve for r |2r-2|=12