Solve: 3(y−5) 4 −4y=3- (y-3) 2 - Vidyadip

Question

Solve: $\frac{3(\text{y}−5)}{4}−4\text{y}=3-\frac{(\text{y}-3)}{2}$

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Answer

$\frac{3(\text{y}−5)}{4}−4\text{y}=3-\frac{(\text{y}-3)}{2}$
$\Rightarrow \frac{3\text{y} - 15}{4} - 4\text{y} = 3 - \frac{\text{y} - 3}{2}$
$\Rightarrow \frac{3\text{y} - 15 - 16\text{y}}{4} = 3 -\frac{ \text{y} - 3}{2} (L.C.M.$ of $4$ and $1$ is $4)$
$\Rightarrow \frac{-13\text{y} − 15}{4} = \frac{6 - \text{y}+ 3}{2} $
$\Rightarrow \frac{-13\text{y} - 15}{4} = \frac{9 - \text{y}}{2}$
$\Rightarrow 2(-13\text{y}-15) = 4(9 - \text{y})$
$\Rightarrow -26\text{y} - 30 = 36 - 4\text{y}$
$\Rightarrow -26\text{y} + 4\text{y} = 36 + 30$
$\Rightarrow-22\text{y}=66$
$\Rightarrow-22\text{y}=66$ (multiplying both the sides with a - ve sign)
$\Rightarrow\text{y} = -\frac{66}{22 }= -3$
$\therefore\text{y} = -3$

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