# Solve for t (3t+1)/5=(t+5)/10+(t-3)/10 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 t+510+t-310-3t+15.
Simplify terms.
Combine the numerators over the common denominator.
t+5+t-310-3t+15=0
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
-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 by 5 and simplify.
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 by -2 and simplify.
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

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