|-2t+3|+3=15

Subtract 3 from both sides of the equation.

|-2t+3|=15-3

Subtract 3 from 15.

|-2t+3|=12

|-2t+3|=12

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

-2t+3=±12

Set up the positive portion of the ± solution.

-2t+3=12

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

Subtract 3 from both sides of the equation.

-2t=12-3

Subtract 3 from 12.

-2t=9

-2t=9

Divide each term by -2 and simplify.

Divide each term in -2t=9 by -2.

-2t-2=9-2

Cancel the common factor of -2.

Cancel the common factor.

-2t-2=9-2

Divide t by 1.

t=9-2

t=9-2

Move the negative in front of the fraction.

t=-92

t=-92

t=-92

Set up the negative portion of the ± solution.

-2t+3=-12

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

Subtract 3 from both sides of the equation.

-2t=-12-3

Subtract 3 from -12.

-2t=-15

-2t=-15

Divide each term by -2 and simplify.

Divide each term in -2t=-15 by -2.

-2t-2=-15-2

Cancel the common factor of -2.

Cancel the common factor.

-2t-2=-15-2

Divide t by 1.

t=-15-2

t=-15-2

Dividing two negative values results in a positive value.

t=152

t=152

t=152

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

t=-92,152

The result can be shown in multiple forms.

Exact Form:

t=-92,152

Decimal Form:

t=-4.5,7.5

Mixed Number Form:

t=-412,712

Solve for t |-2t+3|+3=15