Question

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

• A. $t=\frac{-6}{13}$
• B. $t=\frac{6}{13}$
• C. $t=\frac{13}{3}$
• D. $t=-2$

Answer 1

The correct option is B $t=\frac{6}{13}$

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

$\Rightarrow \frac{3(3t-2)-4(2t-2)}{4\times 3}=\frac{2}{3}-t$ …[Cross-multiplying the denominators on the LHS]

$\Rightarrow \frac{9t-6-8t+8}{12}=\frac{2}{3}-t$ ...[By Distribution Law]

$\Rightarrow \frac{t+2}{12}=\frac{2}{3}-t$

$\Rightarrow \frac{t}{12}+\frac{2}{12}=\frac{2}{3}-t$.

Transposing $x$ terms to one side, we get,

$\Rightarrow \frac{t}{12}+t=\frac{2}{3}-\frac{2}{12}$

$\Rightarrow \frac{t+12t}{12}=\frac{2}{3}-\frac{1}{6}$

$\Rightarrow \frac{13t}{12}=\frac{4-1}{6}$

$\Rightarrow \frac{13t}{12}=\frac{3}{6}$

$\Rightarrow t=\frac{6}{13}$.

Hence, option $B$ is correct.