# Solve for x |2x-3|=y |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
Solve the first equation for x.
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
Solve the second equation for x.
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
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