|2x-3|=y

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

2x-3=±y

Set up the positive portion of the ± solution.

2x-3=y

Add 3 to both sides of the equation.

2x=y+3

Divide each term by 2 and simplify.

Divide each term in 2x=y+3 by 2.

2×2=y2+32

Cancel the common factor of 2.

Cancel the common factor.

2×2=y2+32

Divide x by 1.

x=y2+32

x=y2+32

x=y2+32

x=y2+32

Set up the negative portion of the ± solution.

2x-3=-y

Add 3 to both sides of the equation.

2x=-y+3

Divide each term by 2 and simplify.

Divide each term in 2x=-y+3 by 2.

2×2=-y2+32

Cancel the common factor of 2.

Cancel the common factor.

2×2=-y2+32

Divide x by 1.

x=-y2+32

x=-y2+32

Move the negative in front of the fraction.

x=-y2+32

x=-y2+32

x=-y2+32

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

x=y2+32

x=-y2+32

Solve for x |2x-3|=y