Question
$\frac{\text{x}}{2}-\frac{4}{5}+\frac{\text{x}}{5}+\frac{3\text{x}}{10}=\frac{1}{5}$
✓
Answer
$\frac{\text{x}}{2}-\frac{4}{5}+\frac{\text{x}}{5}+\frac{3\text{x}}{10}=\frac{1}{5}$
Adding to $\frac{4}{5}$ both sides,
$\frac{\text{x}}{2}+\frac{\text{x}}5{}+\frac{3\text{x}}{10}-\frac{4}{5}+\frac{4}{5}=\frac{1}{5}+\frac{4}{5}$
$\Rightarrow\frac{\text{x}}{2}+\frac{\text{x}}{5}+\frac{3\text{x}}{10}-\frac{5}{5}=1$
$\frac{5\text{x}+2\text{x}+3\text{x}}{10}=1$ (L.C.M of 2, 5, 10 = 1)
$\frac{10\text{x}}{10}=1$
$\Rightarrow\text{x}=1$
$\therefore\text{x}=1$
Verification:
$\text{L.H.S}=\frac{\text{x}}{2}-\frac{4}{5}+\frac{\text{x}}{5}+\frac{3\text{x}}{10}$
$=\frac{1}{2}-\frac{4}{5}+\frac{1}{5}+\frac{3}{10}$
$=\frac{5-8+2+3}{10}=\frac{10-8}{10}=\frac{2}{10}$
$=\frac{1}{5}= \text{R.H.S}$
Adding to $\frac{4}{5}$ both sides,
$\frac{\text{x}}{2}+\frac{\text{x}}5{}+\frac{3\text{x}}{10}-\frac{4}{5}+\frac{4}{5}=\frac{1}{5}+\frac{4}{5}$
$\Rightarrow\frac{\text{x}}{2}+\frac{\text{x}}{5}+\frac{3\text{x}}{10}-\frac{5}{5}=1$
$\frac{5\text{x}+2\text{x}+3\text{x}}{10}=1$ (L.C.M of 2, 5, 10 = 1)
$\frac{10\text{x}}{10}=1$
$\Rightarrow\text{x}=1$
$\therefore\text{x}=1$
Verification:
$\text{L.H.S}=\frac{\text{x}}{2}-\frac{4}{5}+\frac{\text{x}}{5}+\frac{3\text{x}}{10}$
$=\frac{1}{2}-\frac{4}{5}+\frac{1}{5}+\frac{3}{10}$
$=\frac{5-8+2+3}{10}=\frac{10-8}{10}=\frac{2}{10}$
$=\frac{1}{5}= \text{R.H.S}$
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