# Solve for y |4y-9|-5=0

|4y-9|-5=0
Add 5 to both sides of the equation.
|4y-9|=5
Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.
4y-9=±5
Set up the positive portion of the ± solution.
4y-9=5
Solve the first equation for y.
Move all terms not containing y to the right side of the equation.
Add 9 to both sides of the equation.
4y=5+9
4y=14
4y=14
Divide each term by 4 and simplify.
Divide each term in 4y=14 by 4.
4y4=144
Cancel the common factor of 4.
Cancel the common factor.
4y4=144
Divide y by 1.
y=144
y=144
Cancel the common factor of 14 and 4.
Factor 2 out of 14.
y=2(7)4
Cancel the common factors.
Factor 2 out of 4.
y=2⋅72⋅2
Cancel the common factor.
y=2⋅72⋅2
Rewrite the expression.
y=72
y=72
y=72
y=72
y=72
Set up the negative portion of the ± solution.
4y-9=-5
Solve the second equation for y.
Move all terms not containing y to the right side of the equation.
Add 9 to both sides of the equation.
4y=-5+9
4y=4
4y=4
Divide each term by 4 and simplify.
Divide each term in 4y=4 by 4.
4y4=44
Cancel the common factor of 4.
Cancel the common factor.
4y4=44
Divide y by 1.
y=44
y=44
Divide 4 by 4.
y=1
y=1
y=1
The solution to the equation includes both the positive and negative portions of the solution.
y=72,1
The result can be shown in multiple forms.
Exact Form:
y=72,1
Decimal Form:
y=3.5,1
Mixed Number Form:
y=312,1
Solve for y |4y-9|-5=0