Question
Solve the following equations. Check your result in case.
$2\text{x}-3=\frac{3}{10}(5\text{x}-12)$
$2\text{x}-3=\frac{3}{10}(5\text{x}-12)$
✓
Answer
$\frac{3\text{x}-3}{1}=\frac{3}{10}(5\text{x}-12)$
$\Rightarrow10(2\text{x}-3)=3(5\text{x}-12)$ (By cross multiplication)
$\Rightarrow20\text{x}-30=15\text{x}-36$
$\Rightarrow20\text{x}-15\text{x}=-36+30$
$\Rightarrow5\text{x}=-6$
$\Rightarrow\text{x}=\frac{-6}{5}$
$\therefore\text{x}=\frac{-6}{5}$
Check
$\text{L.H.S.}=2\text{x}-3=2\times\Big(\frac{-6}{5}\Big)-3$
$=\frac{-12}{5}-\frac{3}{1}=\frac{-12-15}{5}=\frac{-27}{5}$
$\text{R.H.S.}=\frac{3}{10}(5\text{x}-12)$
$=\frac{3}{10}\Big[5\text{x}\Big(\frac{-6}{5}\Big)-12\Big]$
$=\frac{3}{10}(-6-12)=\frac{3}{10}\times(-18)$
$\frac{3\times(-18)}{10}=\frac{3\times(-9)}{5}=\frac{-27}{5}$
$\therefore\text{L.H.S.=R.H.S.}$
Hence $\text{x}=\frac{-6}{5}$
$\Rightarrow10(2\text{x}-3)=3(5\text{x}-12)$ (By cross multiplication)
$\Rightarrow20\text{x}-30=15\text{x}-36$
$\Rightarrow20\text{x}-15\text{x}=-36+30$
$\Rightarrow5\text{x}=-6$
$\Rightarrow\text{x}=\frac{-6}{5}$
$\therefore\text{x}=\frac{-6}{5}$
Check
$\text{L.H.S.}=2\text{x}-3=2\times\Big(\frac{-6}{5}\Big)-3$
$=\frac{-12}{5}-\frac{3}{1}=\frac{-12-15}{5}=\frac{-27}{5}$
$\text{R.H.S.}=\frac{3}{10}(5\text{x}-12)$
$=\frac{3}{10}\Big[5\text{x}\Big(\frac{-6}{5}\Big)-12\Big]$
$=\frac{3}{10}(-6-12)=\frac{3}{10}\times(-18)$
$\frac{3\times(-18)}{10}=\frac{3\times(-9)}{5}=\frac{-27}{5}$
$\therefore\text{L.H.S.=R.H.S.}$
Hence $\text{x}=\frac{-6}{5}$
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