Solve: 2x+7 5 - 3x+11 2 = 2x+8 3 -5 - Vidyadip

Question

Solve:
$\frac{\text{2x}+7}{5}-\frac{\text{3x}+11}{2}=\frac{2\text{x}+8}{3}-5$

✓

Answer

$\frac{\text{2x}+7}{5}-\frac{\text{3x}+11}{2}=\frac{2\text{x}+8}{3}-5$
$\Rightarrow\frac{2\text{x} + 7}{5} - \frac{3\text{x} + 11}{2} = \frac{2\text{x} + 8 - 15}{3} $ $(L.C.M$ of $3$ and $1$ is $3)$
$\Rightarrow30\Big(\frac{2\text{x} + 7}{5}\Big) -30\Big( \frac{3\text{x} + 11}{2}\Big) =30\Big( \frac{2\text{x} + 8 - 15}{3} \Big)$
$($multiplying throughout by $30$, which is the $L.C.M.$ of $5, 2$ and $3)$
$\Rightarrow6 (2\text{x} + 7) - 15 (3\text{x} + 11) = 10 (2\text{x} + 8 - 15) $
$\Rightarrow12\text{x} + 42 -45\text{x} - 165 = 20\text{x} - 70$
$-33\text{x}-123=20\text{x}$

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