Exercise 1- Modulus Functions
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TOPIC 1.1: EQUATIONS AND INEQUALITIES INVOLVING MODULI Ex 1: 1. Solve the following equations, for each case; (a) |x + 2| = 5 (b) |x – 1| = 7 (c) |2x – 3| = 3 (d) |3x + 1| = 10
(e) (f) (g) (h)
2. Solve the following inequalities, for each case; (a) |x + 2| < 1 (e) (b) |x – 3| > 5 (f) (c) |2x + 7| ≤ 3 (g) (h) (d) |3x + 2| ≥ 8 3. Solve the following inequalities, for each case; (g) (a) |2x – 1| > x – 3 (b) |x – 2| < 2x (h) (i) (c) |6 – x| ≤ 3 (j) (d) |15 – x| < 10 (e) |x – 9| ≤ 7 (k) (f) |x – 24| < 8
|x + 1| = |2x + 3| |x + 3| = |3x + 1| |2x + 1| = |3x + 9| |5x + 1| = |11 – 2x| |x + 2| < |3x + 1| |2x + 5| > |x + 2| |x| > |2x + 3| |4x + 1| ≤ |4x – 1| |x + 1| < |x – 2| (Q1 M.Ex 2) |x + 2| > 2x + 1 (Q5) 4|x| > |x – 1| (Q6) |x| < 4|x – 3| (Q9) | x 1 | 4 | x 1 | (Q15c)
(e) (f) (g) (h)
2. Solve the following inequalities, for each case; (a) |x + 2| < 1 (e) (b) |x – 3| > 5 (f) (c) |2x + 7| ≤ 3 (g) (h) (d) |3x + 2| ≥ 8 3. Solve the following inequalities, for each case; (g) (a) |2x – 1| > x – 3 (b) |x – 2| < 2x (h) (i) (c) |6 – x| ≤ 3 (j) (d) |15 – x| < 10 (e) |x – 9| ≤ 7 (k) (f) |x – 24| < 8
|x + 1| = |2x + 3| |x + 3| = |3x + 1| |2x + 1| = |3x + 9| |5x + 1| = |11 – 2x| |x + 2| < |3x + 1| |2x + 5| > |x + 2| |x| > |2x + 3| |4x + 1| ≤ |4x – 1| |x + 1| < |x – 2| (Q1 M.Ex 2) |x + 2| > 2x + 1 (Q5) 4|x| > |x – 1| (Q6) |x| < 4|x – 3| (Q9) | x 1 | 4 | x 1 | (Q15c)
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