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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