3t+15=t+510+t-310

Since t is on the right side of the equation, switch the sides so it is on the left side of the equation.

t+510+t-310=3t+15

Move 3t+15 to the left side of the equation by subtracting it from both sides.

t+510+t-310-3t+15=0

Simplify terms.

Combine the numerators over the common denominator.

t+5+t-310-3t+15=0

Add t and t.

2t+5-310-3t+15=0

Subtract 3 from 5.

2t+210-3t+15=0

Cancel the common factor of 2t+2 and 10.

Factor 2 out of 2t.

2(t)+210-3t+15=0

Factor 2 out of 2.

2(t)+2(1)10-3t+15=0

Factor 2 out of 2(t)+2(1).

2(t+1)10-3t+15=0

Cancel the common factors.

Factor 2 out of 10.

2(t+1)2(5)-3t+15=0

Cancel the common factor.

2(t+1)2⋅5-3t+15=0

Rewrite the expression.

t+15-3t+15=0

t+15-3t+15=0

t+15-3t+15=0

Combine the numerators over the common denominator.

t+1-(3t+1)5=0

t+1-(3t+1)5=0

Simplify the numerator.

Apply the distributive property.

t+1-(3t)-1⋅15=0

Multiply 3 by -1.

t+1-3t-1⋅15=0

Multiply -1 by 1.

t+1-3t-15=0

Subtract 3t from t.

-2t+1-15=0

Subtract 1 from 1.

-2t+05=0

Add -2t and 0.

-2t5=0

-2t5=0

Move the negative in front of the fraction.

-2t5=0

-2t5=0

Since this is the only denominator in the list, the result is the LCD: 5.

5

Multiply each term in -2t5=0 by 5.

-2t5⋅5=0⋅5

Cancel the common factor of 5.

Move the leading negative in -2t5 into the numerator.

-2t5⋅5=0⋅5

Cancel the common factor.

-2t5⋅5=0⋅5

Rewrite the expression.

-2t=0⋅5

-2t=0⋅5

Multiply 0 by 5.

-2t=0

-2t=0

Divide each term in -2t=0 by -2.

-2t-2=0-2

Cancel the common factor of -2.

Cancel the common factor.

-2t-2=0-2

Divide t by 1.

t=0-2

t=0-2

Divide 0 by -2.

t=0

t=0

Solve for t (3t+1)/5=(t+5)/10+(t-3)/10