Question
Solve the following equations. Check your result in case.
$\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}=3$
$\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}=3$
✓
Answer
$\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}=3$
$\Rightarrow\frac{6(\text{x}-9)+7\text{x}=63}{21}$ (LCM of 7, 3 = 21)
$\Rightarrow6\text{x}-54+7\text{x}=63$
$\Rightarrow6\text{x}+7\text{x}=63+54=117$
$\Rightarrow13\text{x}=117$
$\Rightarrow\text{x}=\frac{117}{13}=9$
Check:
$\text{L.H.S.}=\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}$
$=\frac{2}{7}(9-9)+\frac{9}{3}$
$=\frac{2}{7}\times0+3$
$=0+3=3\text{ R.H.S.}$
Hence $\text{x}=9$
$\Rightarrow\frac{6(\text{x}-9)+7\text{x}=63}{21}$ (LCM of 7, 3 = 21)
$\Rightarrow6\text{x}-54+7\text{x}=63$
$\Rightarrow6\text{x}+7\text{x}=63+54=117$
$\Rightarrow13\text{x}=117$
$\Rightarrow\text{x}=\frac{117}{13}=9$
Check:
$\text{L.H.S.}=\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}$
$=\frac{2}{7}(9-9)+\frac{9}{3}$
$=\frac{2}{7}\times0+3$
$=0+3=3\text{ R.H.S.}$
Hence $\text{x}=9$
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