Question

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

Answer 1

$\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$
$\Rightarrow \frac{3t-2}{4}-\frac{2t+3}{3}+t=\frac{2}{3}$
$\Rightarrow \frac{3(3t-2)-4(2t+3)+12t}{12}=\frac{2}{3}$
$\Rightarrow \frac{9t-6-8t-12+12t}{12}=\frac{2}{3}$
$\Rightarrow \frac{13t-18}{12}=\frac{2}{3}$
$\Rightarrow 3\times (13t-18)=2\times 12$
$\Rightarrow 39t-54=24$
$\Rightarrow 39t=24+54$
$\Rightarrow 39t=78$
$\Rightarrow t=\frac{78}{39}=2$