Question
Solve the following equations. Check your result in case.
$\frac{3\text{x}-1}{5}-\frac{\text{x}}{7}=3$
$\frac{3\text{x}-1}{5}-\frac{\text{x}}{7}=3$
✓
Answer
$\frac{21\text{x}-7-5\text{x}}{35}=\frac{3}{1}$ $(LCM$ of $5, 7 = 35)$
$\frac{16\text{x}-7}{35}=\frac{3}{1}$ (By cross multiplication)
$\Rightarrow16\text{x}-7=3\times35$
$\Rightarrow16\text{x}-7=105$
$\Rightarrow16\text{x}=105+7=112$
$\Rightarrow\text{x}=\frac{112}{6}=7$
$\Rightarrow\text{x}=7$
$\therefore\text{x}=7$
Check:
$\text{L.H.S.}=\frac{3\text{x}-1}{5}-\frac{\text{x}}{7}=\frac{3\times7-1}{5}=\frac{-7}{7}$
$=\frac{21-1}{5}-1=\frac{20}{5}-1=4-1=3=\text{R.H.S.}$
Hence $\text{x}=7$
$\frac{16\text{x}-7}{35}=\frac{3}{1}$ (By cross multiplication)
$\Rightarrow16\text{x}-7=3\times35$
$\Rightarrow16\text{x}-7=105$
$\Rightarrow16\text{x}=105+7=112$
$\Rightarrow\text{x}=\frac{112}{6}=7$
$\Rightarrow\text{x}=7$
$\therefore\text{x}=7$
Check:
$\text{L.H.S.}=\frac{3\text{x}-1}{5}-\frac{\text{x}}{7}=\frac{3\times7-1}{5}=\frac{-7}{7}$
$=\frac{21-1}{5}-1=\frac{20}{5}-1=4-1=3=\text{R.H.S.}$
Hence $\text{x}=7$
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