Example 4 Solve (5 − 2𝑥)/3 ≤ 𝑥/6 − 5. (5 − 2𝑥)/3 ≤ 𝑥/6 − 5 (5 − 2𝑥)/3 ≤ (𝑥 − 30)/6 6 × (5 − 2𝑥)/3 ≤ x – 30 2(5 – 2x) ≤ x – 30. 10 – 4x ≤ x – 30 – 4x – x ≤ – 30 – 10 – 5x ≤ – 40 – x ≤ (−40)/( 5) – x ≤ −8 Since x is negative, we multiply both sides by −1 & change the signs (– 1) × (–x) ≥ (– 1) × (–8) x ≥ 8 Hence, x is a real number greater than or equal to 8 Hence, x ∈ [8, ∞) 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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