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Question

Mathematics Question on inequalities

Solve the inequality: −3≤4−7x2≤18-3 ≤ 4-\frac{7x}{2} ≤ 18

Answer

−3≤4−7x2≤18-3 ≤ 4-\frac{7x}{2} ≤ 18
⇒−3−4≤−7x2≤18−4⇒ -3-4 ≤ -\frac{7x}{2} ≤ 18-4
⇒−7≤−7x2≤14⇒ -7 ≤ -\frac{7x}{2} ≤ 14
⇒7≥7x2≥−14⇒ 7 ≥\frac{7x}{2} ≥ -14
⇒1≥x2≥−2⇒ 1 ≥ \frac{x}{2} ≥ -2
⇒2≥x≥−4⇒ 2 ≥ x ≥ -4
Thus, the solution set for the given inequality is [–4, 2].