|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

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

Add 3 to both sides of the equation.

2t=6+3

Add 6 and 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

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

Add 3 to both sides of the equation.

2t=-6+3

Add -6 and 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