Question:
$\frac{2(x-1)}{5} \leq \frac{3(2+x)}{7}$
Solution:
$\frac{2(x-1)}{5} \leq \frac{3(2+x)}{7}$
$\Rightarrow 14(x-1) \leq 15(2+x)$
$\Rightarrow 14 x-14 \leq 30+15 x$
$\Rightarrow 30+15 x \geq 14 x-14$
$\Rightarrow 15 x-14 x \geq-14-30 \quad$ (Transposing $14 x$ to the LHS and 30 to the RHS)
$\Rightarrow x \geq-44$
Hence, the solution to the given inequation is $[-44, \infty)$.
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