2x 15 #8804;32+x7 #8658;14x 1 #8804;152+x #160; #8658;14x 14 #8804;30+15x #8658;30+15x #8805;14x 14 #8658;15x 14x #8805; 14 30 #160; #16 ...

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Method of Intervals

2 x-15 ≤ 32+x...

Question

$\frac{2 (x - 1)}{5} \leq \frac{3 (2 + x)}{7}$

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Solution

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

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