Question

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

Answer 1

$\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$
L.C.M. of the denominators, $3$ and $4$, is $12$.
Multiplying both sides by $12$, we obtain
$3(3t - 2) - 4(2t + 3) = 8 - 12t$
$\Rightarrow$ $9t - 6 - 8t - 12 = 8 - 12t$ (Opening the brackets)
$\Rightarrow$ $9t - 8t + 12t = 8 + 6 + 12$
$\Rightarrow$ $13t = 26$
$\Rightarrow$ $t$ = $\frac{26}{13}$
$\Rightarrow$ $t = 2$