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Mathematics

Solve 1 ≥ 15 - 7x > 2x - 27, x ∈ N.

Linear Inequations

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Answer

Given,

1≥15−7x>2x−27⇒1≥15−7x and 15−7x>2x−27⇒7x≥15−1 and −7x−2x>−27−15⇒7x≥14 and −9x>−42⇒x≥2 and −x>−429⇒x≥2 and x<143⇒2≤x<1431 \ge 15 - 7x \gt 2x - 27\\[0.5em] \Rightarrow 1 \ge 15 - 7x \text{ and } 15 - 7x \gt 2x - 27\\[0.5em] \Rightarrow 7x \ge 15-1 \text{ and } -7x-2x \gt -27-15\\[0.5em] \Rightarrow 7x \ge 14 \text{ and } -9x \gt -42\\[0.5em] \Rightarrow x \ge 2 \text{ and } -x \gt -\dfrac{42}{9}\\[0.5em] \Rightarrow x \ge 2 \text{ and } x \lt \dfrac{14}{3}\\[0.5em] \Rightarrow 2 \le x \lt \dfrac{14}{3}

Since x ∈ N,

Solution set = {2, 3, 4}.

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