Question
Solve the following equations. Check your result in case. $0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
✓
Answer
$0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
$\Rightarrow\frac{5}{10}\text{x}+\frac{\text{x}}{3}=\frac{25}{100}\text{x}+7$
$\Rightarrow\frac{1}{2}\text{x}+\frac{\text{x}}{3}=\frac{\text{x}}{4}=7$
$\Rightarrow\frac{1}{2}\text{x}+\frac{1}{3}\text{x}-\frac{1}{4}\text{x}=7$
$\Rightarrow\frac{6\text{x}+4\text{x}-3\text{x}}{12}=7$
$\Rightarrow\frac{7\text{x}}{12}=7$
$\Rightarrow\text{x}=\frac{7\times12}{7}=12$
$\therefore\text{x}=12$
Check: $\text{L.H.S.}=0.5\text{x}+\frac{\text{x}}{3}$
$=\frac{1}{2}\text{x}+\frac{\text{x}}{3}$
$=\frac{12}{2}+\frac{12}{3}$
$=6+4$
$=10$
$\text{R.H.S.}=0.25\text{x}+7$
$=\frac{1}{4}\times12+7$
$=3+7$
$=10$
$\therefore\text{L.H.S. = R.H.S.}$
Hence $\text{x}=12$
$\Rightarrow\frac{5}{10}\text{x}+\frac{\text{x}}{3}=\frac{25}{100}\text{x}+7$
$\Rightarrow\frac{1}{2}\text{x}+\frac{\text{x}}{3}=\frac{\text{x}}{4}=7$
$\Rightarrow\frac{1}{2}\text{x}+\frac{1}{3}\text{x}-\frac{1}{4}\text{x}=7$
$\Rightarrow\frac{6\text{x}+4\text{x}-3\text{x}}{12}=7$
$\Rightarrow\frac{7\text{x}}{12}=7$
$\Rightarrow\text{x}=\frac{7\times12}{7}=12$
$\therefore\text{x}=12$
Check: $\text{L.H.S.}=0.5\text{x}+\frac{\text{x}}{3}$
$=\frac{1}{2}\text{x}+\frac{\text{x}}{3}$
$=\frac{12}{2}+\frac{12}{3}$
$=6+4$
$=10$
$\text{R.H.S.}=0.25\text{x}+7$
$=\frac{1}{4}\times12+7$
$=3+7$
$=10$
$\therefore\text{L.H.S. = R.H.S.}$
Hence $\text{x}=12$
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