Example 18 Solve the system of inequalities: 3x – 7 < 5 + x 11 – 5 x ≤ 1 and represent the solutions on the number line. Solving 3x – 7 < 5 + x 3x – x < 5 + 7 2x < 12 x < 12/2 x < 6 Solving 11 – 5x ≤ 1 – 5x ≤ 1 – 11 – 5x ≤ – 10 – x ≤ (−10)/5 – x ≤ −2 Since x is negative, we multiply both sides by -1 & change the signs (– 1) × (-x) ≥ (–1) × (–2) x ≥ 2 Thus, x < 6 & x ≥ 2 The graphical representation is Here 2 is included in the shaded graph & 6 is not included The solution is 2 ≤ x < 6

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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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