Solve the following linear inequations in R: 2(x-1) 5 3(2+x) 7 - Vidyadip

Question

Solve the following linear inequations in R: $\frac{2(\text{x}-1)}{5}\leq\frac{3(2+\text{x})}{7}$

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Answer

$\frac{2(\text{x}-1)}{5}\leq\frac{3(2+\text{x})}{7}$ $\Rightarrow7(2(\text{x}-1))\leq5(3(2+\text{x}))$ $14(\text{x}-1)\leq15(2+\text{x})$ $\Rightarrow14\text{x}-14\leq30+15\text{x}$ $\Rightarrow14\text{x}-15\text{x}\leq30+14$ $\Rightarrow-\text{x}\leq44$ $\Rightarrow\text{x}\geq-44$ $\therefore$ The solution set is $[-44,\infty)$

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