3-|y+9|=11-3|y+9|

Add 3|y+9| to both sides of the equation.

3-|y+9|+3|y+9|=11

Add -|y+9| and 3|y+9|.

3+2|y+9|=11

3+2|y+9|=11

Subtract 3 from both sides of the equation.

2|y+9|=11-3

Subtract 3 from 11.

2|y+9|=8

2|y+9|=8

Divide each term in 2|y+9|=8 by 2.

2|y+9|2=82

Cancel the common factor of 2.

Cancel the common factor.

2|y+9|2=82

Divide |y+9| by 1.

|y+9|=82

|y+9|=82

Divide 8 by 2.

|y+9|=4

|y+9|=4

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

y+9=±4

Set up the positive portion of the ± solution.

y+9=4

Subtract 9 from both sides of the equation.

y=4-9

Subtract 9 from 4.

y=-5

y=-5

Set up the negative portion of the ± solution.

y+9=-4

Subtract 9 from both sides of the equation.

y=-4-9

Subtract 9 from -4.

y=-13

y=-13

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

y=-5,-13

Solve for y 3-|y+9|=11-3|y+9|