Solve the following
Question:

$\frac{5-2 x}{3}<\frac{x}{6}-5$

Solution:

$\frac{5-2 x}{3}<\frac{x}{6}-5$

$\Rightarrow \frac{5-2 x}{3}-\frac{x}{6}<-5 \quad\left[\right.$ Transposing $\frac{x}{6}$ to the LHS $]$

$\Rightarrow \frac{2(5-2 \mathrm{x})-\mathrm{x}}{6}<-5$

$\Rightarrow \frac{10-4 \mathrm{x}-\mathrm{x}}{6}<-5$

$\Rightarrow \frac{10-5 \mathrm{x}}{6}<-5$

$\Rightarrow 10-5 x<-30$

$\Rightarrow 10+30<5 x$

$\Rightarrow 40<5 x$

$\Rightarrow 5 x>40$

$\Rightarrow x>\frac{40}{5}$

$\Rightarrow x>8$

Hence, the solution set of the given inequality is $(8, \infty)$.

 

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