1+10|7y+7|=71

Subtract 1 from both sides of the equation.

10|7y+7|=71-1

Subtract 1 from 71.

10|7y+7|=70

10|7y+7|=70

Divide each term in 10|7y+7|=70 by 10.

10|7y+7|10=7010

Cancel the common factor of 10.

Cancel the common factor.

10|7y+7|10=7010

Divide |7y+7| by 1.

|7y+7|=7010

|7y+7|=7010

Divide 70 by 10.

|7y+7|=7

|7y+7|=7

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

7y+7=±7

Set up the positive portion of the ± solution.

7y+7=7

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

Subtract 7 from both sides of the equation.

7y=7-7

Subtract 7 from 7.

7y=0

7y=0

Divide each term by 7 and simplify.

Divide each term in 7y=0 by 7.

7y7=07

Cancel the common factor of 7.

Cancel the common factor.

7y7=07

Divide y by 1.

y=07

y=07

Divide 0 by 7.

y=0

y=0

y=0

Set up the negative portion of the ± solution.

7y+7=-7

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

Subtract 7 from both sides of the equation.

7y=-7-7

Subtract 7 from -7.

7y=-14

7y=-14

Divide each term by 7 and simplify.

Divide each term in 7y=-14 by 7.

7y7=-147

Cancel the common factor of 7.

Cancel the common factor.

7y7=-147

Divide y by 1.

y=-147

y=-147

Divide -14 by 7.

y=-2

y=-2

y=-2

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

y=0,-2

Solve for y 1+10|7y+7|=71