# Solve for y |y-23|-|y-29|=0 |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)
Solve y-23=y-29 for y.
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
Solve y-23=-(y-29) for y.
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
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
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

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