132 Chapter 2 Expressions and linear equations Exercise 2G FLUENCY 1−6( 1/2) 1−6( 1/3) 1. Show each of the following inequalities on a number line. a. x > 2 b. x ⩽ 4 d. − 1 < x < 1 e. 0 ⩽ x ⩽ 3 c. x ⩾ − 1 f. − 3 < x ⩽ 4 2. Find the solution set for each of the following inequalities. a. x + 5 < 8 b. b − 2 > 3 d. 5x ⩾ 15 e. 4t > − 20 g. 3m − 7 < 11 h. 4a + 6 ⩾ 12 c. y − 8 > − 2 f. y + 10 ⩾ 0 i. 7x − 5 < 2 3. Find the solution set for each of the following inequalities. a. 4 − 3x > − 8 b. 2 − 4n ⩾ 6 d. 7 − a ⩽ 3 e. 5 − x ⩽ 11 g. − 2x − 3 > 9 h. − 4t + 2 ⩾ 10 c. 4 − 5x ⩽ 1 f. 7 − x ⩽ − 3 i. − 6m − 14 < 15 4. Find the solution set for each of the following inequalities. a. _ x − 5 ⩽ 3 b. 3 − _x ⩾ 4 2 9 3x − 4 > − 6 2x + 6 e. _ d. _ < 4 2 7 2x ⩽ 8 c. _ 5 1 _ f. − 7x ⩽ 3 5 5. Solve these inequalities involving brackets. a. 4(x + 2) < 12 b. − 3(a + 5) > 9 d. 2(3 − x) > 1 e. 5(y + 2) < − 6 c. 5 (3 − x) ⩾ 25 f. − 7(1 − x) < − 11 6. Find the solution set for each of the following inequalities. a. 2x + 9 ⩽ 6x − 1 b. 6t + 2 > t − 1 d. 3a − 2 < 4 − 2a e. 1 − 3m ⩾ 7 − 4m c. 7 y + 4 ⩽ 7 − y f. 7 − 5b > − 4 − 3b U N SA C O M R PL R E EC PA T E G D ES Example 16 1, 2−4(1/2) Example 17a Example 17b Example 17c Example 17d PROBLEM–SOLVING 7−9 8−10 9−11 7. Willow is xyears old and Jay is 6years younger. The sum of their ages is less than 30. Write an inequality involving xand solve it. What can you say about Willow’s age? 8. The perimeter of a particular rectangle needs to be less than 50 cm. If the length of the rectangle is 12 cmand the width is w cm, write an inequality involving wand solve it. What width does the rectangle need to be? P < 50 cm w cm 12 cm 9. How many integers satisfy both of the given inequalities? a. 2x + 1 ⩽ 5and 5 − 2x ⩽ 5 b. 7 − 3x > 10and 5x + 13 > − 5 x + 1 5x + 1 < 2and _x < 2x − 7 x _ _ c. ⩾ − 2and 2 − > 3 d. _ 3 3 3 6 10. The width of a rectangular area is 10 mand its height is (2x − 4) m. If the area is less than 80 m2 , what are the possible integer values for x? Uncorrected 3rd sample pages • Cambridge University Press & Assessment • Greenwood, et al 2025 • 978-1-009-65757-0 • (03) 8671 1400