Question
$\frac{\text{x}}{2}+\frac{\text{x}}{8}=\frac{1}{8}$
✓
Answer
$\frac{\text{x}}{2}+\frac{\text{x}}{8}=\frac{1}{8}$
$\frac{4\text{x}+\text{x}}{8}=\frac{1}{8}$ $(L.C.M$ of $2, 8 = 8)$
$\frac{5\text{x}}{8}=\frac{1}{8}$
Dividing by $\frac{5}{8}$
$\frac{5}{8}\text{x}+\frac{5}{8}=\frac{1}{8}+\frac{5}{8}$
$\Rightarrow\frac{5}{8}\text{x}\times\frac{8}{5}=\frac{1}{8}\times\frac{5}{8}$
$\Rightarrow\text{x}=\frac{1}{5}$
$\therefore\text{x}=\frac{1}{5}$
Verification:
$\text{L.H.S}$ $=\frac{\text{x}}{2}+\frac{\text{x}}{8}$
$=\frac{\frac{1}{5}}{2}+\frac{\frac{1}{5}}{8}=\frac{1}{5\times2}+\frac{1}{5\times8}$
$=\frac{1}{10}+\frac{1}{40}=\frac{4+1}{40}=\frac{5}{40}$
$=\frac{1}{8}=\text{R.H.S}$
$\frac{4\text{x}+\text{x}}{8}=\frac{1}{8}$ $(L.C.M$ of $2, 8 = 8)$
$\frac{5\text{x}}{8}=\frac{1}{8}$
Dividing by $\frac{5}{8}$
$\frac{5}{8}\text{x}+\frac{5}{8}=\frac{1}{8}+\frac{5}{8}$
$\Rightarrow\frac{5}{8}\text{x}\times\frac{8}{5}=\frac{1}{8}\times\frac{5}{8}$
$\Rightarrow\text{x}=\frac{1}{5}$
$\therefore\text{x}=\frac{1}{5}$
Verification:
$\text{L.H.S}$ $=\frac{\text{x}}{2}+\frac{\text{x}}{8}$
$=\frac{\frac{1}{5}}{2}+\frac{\frac{1}{5}}{8}=\frac{1}{5\times2}+\frac{1}{5\times8}$
$=\frac{1}{10}+\frac{1}{40}=\frac{4+1}{40}=\frac{5}{40}$
$=\frac{1}{8}=\text{R.H.S}$
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