# Solve for t |2t-3|=6 |2t-3|=6
Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.
2t-3=±6
Set up the positive portion of the ± solution.
2t-3=6
Solve the first equation for t.
Move all terms not containing t to the right side of the equation.
Add 3 to both sides of the equation.
2t=6+3
2t=9
2t=9
Divide each term by 2 and simplify.
Divide each term in 2t=9 by 2.
2t2=92
Cancel the common factor of 2.
Cancel the common factor.
2t2=92
Divide t by 1.
t=92
t=92
t=92
t=92
Set up the negative portion of the ± solution.
2t-3=-6
Solve the second equation for t.
Move all terms not containing t to the right side of the equation.
Add 3 to both sides of the equation.
2t=-6+3
2t=-3
2t=-3
Divide each term by 2 and simplify.
Divide each term in 2t=-3 by 2.
2t2=-32
Cancel the common factor of 2.
Cancel the common factor.
2t2=-32
Divide t by 1.
t=-32
t=-32
Move the negative in front of the fraction.
t=-32
t=-32
t=-32
The solution to the equation includes both the positive and negative portions of the solution.
t=92,-32
The result can be shown in multiple forms.
Exact Form:
t=92,-32
Decimal Form:
t=4.5,-1.5
Mixed Number Form:
t=412,-112
Solve for t |2t-3|=6

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