Question
Solve $\frac{3 t-2}{3}+\frac{2 t+3}{2}=t+\frac{7}{6}$
✓
Answer
We have, $\frac{3 t-2}{3}+\frac{2 t+3}{2}=t+\frac{7}{6}$
$\Rightarrow \quad \frac{3 t-2}{3}+\frac{2 t+3}{2}-\frac{t}{1}=\frac{7}{6}\quad$ [transposing $t$ to LHS]
$\Rightarrow \frac{2 \times(3 t-2)+3 \times(2 t+3)-6 \times t}{6}=\frac{7}{6}$
$\Rightarrow \quad \frac{6 t-4+6 t+9-6 t}{6}=\frac{7}{6}$
$\Rightarrow \quad \frac{6 t+5}{6}=\frac{7}{6}$
$\Rightarrow \quad(6 t+5)=\frac{7 \times 6}{6}\quad$ [multiplying both sides by 6]
$\Rightarrow \quad 6 t+5=7$
$\Rightarrow \quad 6 t=7-5=2\quad$ [transposing 5 to RHS]
$\therefore \quad t=\frac{2}{6}=\frac{1}{3}$
$\Rightarrow \quad \frac{3 t-2}{3}+\frac{2 t+3}{2}-\frac{t}{1}=\frac{7}{6}\quad$ [transposing $t$ to LHS]
$\Rightarrow \frac{2 \times(3 t-2)+3 \times(2 t+3)-6 \times t}{6}=\frac{7}{6}$
$\Rightarrow \quad \frac{6 t-4+6 t+9-6 t}{6}=\frac{7}{6}$
$\Rightarrow \quad \frac{6 t+5}{6}=\frac{7}{6}$
$\Rightarrow \quad(6 t+5)=\frac{7 \times 6}{6}\quad$ [multiplying both sides by 6]
$\Rightarrow \quad 6 t+5=7$
$\Rightarrow \quad 6 t=7-5=2\quad$ [transposing 5 to RHS]
$\therefore \quad t=\frac{2}{6}=\frac{1}{3}$
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