Question
Solve:
$5\text{x}-\frac{1}{3}(\text{x}+1)=6(\text{x}+\frac{1}{30})$
$5\text{x}-\frac{1}{3}(\text{x}+1)=6(\text{x}+\frac{1}{30})$
✓
Answer
$5\text{x}-\frac{1}{3}(\text{x}+1)=6(\text{x}+\frac{1}{30})$$\Rightarrow\text{5x}-\frac{1(\text{x}+1)}{3}=6\Big(\frac{30\text{x}+1}{30}\Big)$ $(\text{L.C.M}\text{ of }1\text{ and }30\text{ is }30)$
$\Rightarrow5\text{x}-\frac{(\text{x}+1)}{3}=\frac{30\text{x}+1}{5}$
$\Rightarrow\frac{15\text{x}-\text{x}-1}{3}=\frac{30\text{x}+1}{5}$ $(\text{L.C.M}\text{ of }1\text{ and }3\text{ is }3)$
$\Rightarrow\frac{14\text{x}-1}{3}=\frac{30\text{x}+1}{5}$
$\Rightarrow5(14\text{x}-1)=3(30\text{x}+1)$ $(\text{by cross multiplication})$
$\Rightarrow70\text{x}-5=90\text{x}+3$
$\Rightarrow70\text{x}-90\text{x}=3+5$
$\Rightarrow-20\text{x}=8$
$\Rightarrow\text{x}=\frac{8}{-20}=\frac{-2}{5}$
$\therefore\text{x}=-\frac{2}{5}$
$\Rightarrow5\text{x}-\frac{(\text{x}+1)}{3}=\frac{30\text{x}+1}{5}$
$\Rightarrow\frac{15\text{x}-\text{x}-1}{3}=\frac{30\text{x}+1}{5}$ $(\text{L.C.M}\text{ of }1\text{ and }3\text{ is }3)$
$\Rightarrow\frac{14\text{x}-1}{3}=\frac{30\text{x}+1}{5}$
$\Rightarrow5(14\text{x}-1)=3(30\text{x}+1)$ $(\text{by cross multiplication})$
$\Rightarrow70\text{x}-5=90\text{x}+3$
$\Rightarrow70\text{x}-90\text{x}=3+5$
$\Rightarrow-20\text{x}=8$
$\Rightarrow\text{x}=\frac{8}{-20}=\frac{-2}{5}$
$\therefore\text{x}=-\frac{2}{5}$
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