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Misc 2 Solve the inequality 6 ≤ –3(2x – 4) < 12 6 ≤ – 3(2x – 4) < 12 6 ≤ – 6x + 12 < 12 Subtracting 12 all sides (Eliminating 12) 6 – 12 ≤ – 6x + 12 – 12 < 12 – 12 –6 ≤ – 6x < 0 Dividing 6 all sides (Eliminating 6) (−6)/( 6) ≤ (−6𝑥)/6 < 0/6 −1 ≤ −𝑥 < 0 Since x is negative, we multiply both sides by -1 & change the signs (– 1) × (–1) ≥ (–1) × (–x) > (–1) × (0) 1 ≥ x > 0 0 < x ≤ 1 Thus, x is a real number which is less than or equal to 1 and greater than 0 Hence, x ∈ (0, 1] is the solution

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo