Answer
t=29
Work Step by Step
$\frac{3t+1}{8}=\frac{5+2t}{7}+2$
Multiply each side by 56, the least common multiple, to eliminate fractions.
$56(\frac{3t+1}{8})=56(\frac{5+2t}{7})+(56)(2)$
$7(3t+1)=8(5+2t)+112$
Apply the distributive property.
$21t+7=40+16t+112$
Combine like terms.
$21t+7=16t+152$
Subtract 16t from both sides. Subtract 7 from both sides.
$21t+7-16t=16t+152-16t$
$5t+7=152$
$5t+7-7=152-7$
$5t=145$
Divide both sides by 5.
$5t\div5=145\div5$
$t=29$