Solve the following

Question:

$2(3-x) \geq \frac{x}{5}+4$

Solution:

$2(3-x) \geq \frac{x}{5}+4$

$\Rightarrow 6-2 x \geq \frac{x}{5}+4$

$\Rightarrow 6-4 \geq \frac{x}{5}+2 x \quad[$ Transposing $-2 x$ to the RHS and 4 to the LHS $]$

$\Rightarrow 2 \geq \frac{11 x}{5}$

$\Rightarrow \frac{11 x}{5} \leq 2$

$\Rightarrow x \leq \frac{10}{11} \quad\left[\right.$ Mltiplying both the sides by $\left.\frac{5}{11}\right]$

Thus, the solution set of the given inequation is $\left(-\infty, \frac{10}{11}\right]$.

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