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Performing Mathematical Operations on Equation

3 x-25 ≤ 4 x-...

Question

$\frac{3 x - 2}{5} \leq \frac{4 x - 3}{2}$

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Solution

$\frac{3 x - 2}{5} \leq \frac{4 x - 3}{2} \Rightarrow 2 (3 x - 2) \leq 5 (4 x - 3) \Rightarrow 6 x - 4 \leq 20 x - 15 \Rightarrow - 4 + 15 \leq 20 x - 6 x (Transposing 6 x to the RHS and - 15 to the LHS) \Rightarrow 11 \leq 14 x \Rightarrow 14 x \geq 11 \Rightarrow x \geq \frac{11}{14} (Dividing both the sides by 14) Hence, the solution set of the given inequation is [\frac{11}{14}, \infty) .$

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