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

|-2t+3|+3=15
Move all terms not containing |-2t+3| to the right side of the equation.
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
Solve the first equation for t.
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
Solve the second equation for t.
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

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