Question

Solve:
$\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$

Answer 1

Given: $\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$
LCM of $3,4$ is $3\times 4=12$
$\Rightarrow \frac{3(3t-2)}{12}-\frac{4(2t+3)}{12}=\frac{2-3t}{3}$
$\Rightarrow \frac{9t-6}{12}-\frac{8t+12}{12}=\frac{2-3t}{3}$
$\Rightarrow \frac{9t-6-8t-12}{12}=\frac{2-3t}{3}$
$\Rightarrow t-18=\frac{12(2-3t)}{3}$
$\Rightarrow t-18=4(2-3t)$
$\Rightarrow t-18=8-12t$
$\Rightarrow 12t+t=8+18$
$\Rightarrow 13t=26$
$\therefore t=2$