# Solve the following

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 $[-44, \infty)$.