Question
Solve the following equations. Check your result in case.
$\frac{\text{x}}{2}+\frac{\text{x}}{4}=\frac{1}{8}$
$\frac{\text{x}}{2}+\frac{\text{x}}{4}=\frac{1}{8}$
✓
Answer
$\frac{\text{x}}{2}+\frac{\text{x}}{4}=\frac{1}{8}$
$\frac{2\text{x}+\text{x}}{4}=\frac{1}{8}$
$\Rightarrow\frac{3\text{x}}{4}=\frac{1}{8}$
$\Rightarrow\text{x}=\frac{1}{8}\times\frac{4}{3}=\frac{1}{6}$
$\therefore\text{x}=\frac{1}{6}$
Check:
$\text{L.H.S.}=\frac{\text{x}}{2}+\frac{\text{x}}{4}$
$=\frac{1}{6\times2}+\frac{1}{6\times4}=\frac{1}{12}+\frac{1}{24}$
$=\frac{2+1}{24}=\frac{3}{24}=\frac{1}{8}=\text{R.H.S.}$
Hence $\text{x}=\frac{1}{6}$
$\frac{2\text{x}+\text{x}}{4}=\frac{1}{8}$
$\Rightarrow\frac{3\text{x}}{4}=\frac{1}{8}$
$\Rightarrow\text{x}=\frac{1}{8}\times\frac{4}{3}=\frac{1}{6}$
$\therefore\text{x}=\frac{1}{6}$
Check:
$\text{L.H.S.}=\frac{\text{x}}{2}+\frac{\text{x}}{4}$
$=\frac{1}{6\times2}+\frac{1}{6\times4}=\frac{1}{12}+\frac{1}{24}$
$=\frac{2+1}{24}=\frac{3}{24}=\frac{1}{8}=\text{R.H.S.}$
Hence $\text{x}=\frac{1}{6}$
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