1 2 (x+1 )+1 3 (x-1)=5 12 (x-2) - Vidyadip

Question

$\frac{1}{2}\Big(\text{x}+1\Big)+\frac{1}{3}(\text{x}-1)=\frac{5}{12}(\text{x}-2)$

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Answer

Given, $\frac{1}{2}\Big(\text{x}+1\Big)+\frac{1}{3}(\text{x}-1)=\frac{5}{12}(\text{x}-2)$$\frac{\text{x}}{2}+\frac{1}{2}+\frac{\text{x}}{3}-\frac{1}{3}=\frac{5\text{x}}{12}-\frac{5}{6}$
$\frac{\text{x}}{2}+\frac{\text{x}}{3}-\frac{5\text{x}}{12}=\frac{1}{3}-\frac{1}{2}-\frac{5}{6}$
$\frac{6\text{x}+4\text{x}-5\text{x}}{12}=\frac{2-3-5}{6}$
$\frac{5\text{x}}{12}=-\frac{6}{6}$
$5\text{x}\times6=(-6)\times12$
$\text{x}=\frac{(-6)\times12}{5\times6}$
$\text{x}=-\frac{12}{5}$

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