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