|y-23|-|y-29|=0

Add |y-29| to both sides of the equation.

|y-23|=|y-29|

Rewrite the absolute value equation as four equations without absolute value bars.

y-23=y-29

y-23=-(y-29)

-(y-23)=y-29

-(y-23)=-(y-29)

After simplifying, there are only two unique equations to be solved.

y-23=y-29

y-23=-(y-29)

Move all terms containing y to the left side of the equation.

Subtract y from both sides of the equation.

y-23-y=-29

Combine the opposite terms in y-23-y.

Subtract y from y.

0-23=-29

Subtract 23 from 0.

-23=-29

-23=-29

-23=-29

Since -23≠-29, there are no solutions.

No solution

No solution

Simplify -(y-29).

Apply the distributive property.

y-23=-y–29

Multiply -1 by -29.

y-23=-y+29

y-23=-y+29

Move all terms containing y to the left side of the equation.

Add y to both sides of the equation.

y-23+y=29

Add y and y.

2y-23=29

2y-23=29

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

Add 23 to both sides of the equation.

2y=29+23

Add 29 and 23.

2y=52

2y=52

Divide each term by 2 and simplify.

Divide each term in 2y=52 by 2.

2y2=522

Cancel the common factor of 2.

Cancel the common factor.

2y2=522

Divide y by 1.

y=522

y=522

Divide 52 by 2.

y=26

y=26

y=26

List all of the solutions.

y=26

Verify each of the solutions by substituting them into |y-23|-|y-29|=0 and solving.

y=26

Solve for y |y-23|-|y-29|=0