Solve: 3t-2 4 - 2t+3 3 =2 3 -t - Vidyadip

Question

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

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Answer

$\frac{\text{3t}-2}{4}-\frac{\text{2t}+3}{3}=\frac{2}{3}-\text{t}$$\Rightarrow\frac{\text{3t}-2}{4}-\frac{\text{2t}+3}{3}=\frac{2-3\text{t}}{3}$ (3 is the L.C.M. of 1 and 3)
$\Rightarrow12\Big(\frac{\text{3t}-2}{4}\Big)-12\Big(\frac{\text{2t}+3}{3}\Big)=12\Big(\frac{2-3\text{t}}{3}\Big)$
(multiplying throughout by 12, which is the L.C.M. of 4, 3 and 3):
$\Rightarrow3(3\text{t}-2)-4(2\text{t}+3)=4(2-3\text{t})$
$\Rightarrow9\text{t} - 6 - 8\text{t} - 12 = 8 - 12\text{t}$
$\Rightarrow 9\text{t} - 8\text{t} - 6 - 12 = 8 - 12\text{t}$
$\Rightarrow\text{t} - 18 = 8 - 12\text{t}$
$\Rightarrow\text{t} + 12\text{t} = 18 + 8$
$\Rightarrow13\text{t} = 26$
$\Rightarrow\text{t} = \frac{26}{13} = 2$
$\therefore \text{t} = 2$

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