|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

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

Add 9 to both sides of the equation.

4y=5+9

Add 5 and 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

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

Add 9 to both sides of the equation.

4y=-5+9

Add -5 and 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