Question

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

Answer 1

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

LCM of $3$ and $4$ is $12$
Multiply both sides by $12$
$\left(\frac{3t-2}{4}\right)12-\left(\frac{2t+3}{3}\right)12=(\frac{2}{3}-t)12$

$3(3t-2)-4(2t+3)$ $=8-12t$

$9t-6-8t-12=8-12t$
$t-18=8-12t$
Transpose $12t$ to LHS and $48$ to RHS
$t+12t=8+18$

$13t=26$
$t=\frac{26}{13}=2$