Question
Solve: $\frac{\text{5x}-4}{6}=\text{4x}+1-\frac{3\text{z}+10}{2}$
✓
Answer
$\frac{\text{5x}-4}{6}=\text{4x}+1-\frac{3\text{z}+10}{2}$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{2(4\text{x}+1)-3\text{x}-10}{2}$
$(\text{L.C.M}\text{ of }1\text{ and }2\text{ is }2)$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{8\text{x}+2-3\text{x}-10}{2}$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{8\text{x}-3\text{x}+2-10}{2}$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{5\text{x}-8}{2}$
$\Rightarrow2(5\text{x}-4)=6(5\text{x}-8)$
$\Rightarrow10\text{x}-8=30\text{x}-48$
$\Rightarrow10\text{x}-30\text{x}=-48+8$
$\Rightarrow10\text{x}-30\text{x}=-48+8$
$\Rightarrow-20\text{x}=-40$
$\Rightarrow\text{x}=\frac{-40}{-20}=2$
$\therefore\text{x}=2$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{2(4\text{x}+1)-3\text{x}-10}{2}$
$(\text{L.C.M}\text{ of }1\text{ and }2\text{ is }2)$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{8\text{x}+2-3\text{x}-10}{2}$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{8\text{x}-3\text{x}+2-10}{2}$
$\Rightarrow\frac{5\text{x}-4}{6}=\frac{5\text{x}-8}{2}$
$\Rightarrow2(5\text{x}-4)=6(5\text{x}-8)$
$\Rightarrow10\text{x}-8=30\text{x}-48$
$\Rightarrow10\text{x}-30\text{x}=-48+8$
$\Rightarrow10\text{x}-30\text{x}=-48+8$
$\Rightarrow-20\text{x}=-40$
$\Rightarrow\text{x}=\frac{-40}{-20}=2$
$\therefore\text{x}=2$
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