Review Exercise 37

Subjective Questions

1. State whether each of the following statements is true or false.(a) 7 > 2 is equivalent to 2 < 7.(b) −4 < −1 is equivalent to 1 > −4.(c) −p < x is equivalent to −x > p.(d) q > x is equivalent to x < q.

2. If x is a positive integer less than 10, state the possible values of x that satisfy the following inequalities.(a) x > 6(b) x < 4(c) 5 < x(d) 7 > x

3. Write a linear inequality to represent each of the following statements.(a) s is greater than or equal to 10.(b) −p is less than 8.(c) 14 is greater than −w.(d) 2 is less than or equal to x.

4. Represent each of the following inequalities on a number line.(a) x ≥ −3(b) x < 1(c) 5 < x(d) −7 ≥ x

5. Copy and complete.(a) If p > 30, then

(i) p + > 44(ii) p + > 25

(b) If q ≤ −14, then(i) q − ≤ −8(ii) q − ≤ −21

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Review Exercise 37

(c) If < 2, then

(i) x < 6

(ii) r < 18(d) If 4s ≥ −24, then

(i) ≥ −12

(ii) s ≥ −6

6. State an inequality in the form x > k or x < k which is equivalent to each of the following inequalities.

(a) − x > 6

(b) −5x < 0

(c) − < −4

(d) −7x > −21

7. Write down the solution for the following inequalities.(a) −x ≥ 6(b) −x < −3(c) −x ≤ 11(d) −x > −18

8. Solve the following inequalities.(a) 3 − x ≤ 8(b) −7 − x > 0(c) 10 − x ≥ −13(d) −14 − x < −20

9. Solve the following inequalities.

(a) − x ≤ 6

(b) − x > −12

(c) x < −

(d) − x ≥ −

10. Determine the solution for each of the following linear inequalities.(a) 2x − 1 > 9(b) 6x + 2 ≤ −10

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Review Exercise 37

(c) 7 − 4x ≥ 3

(d) −3 − x < −5

11. List all the integer values of f that satisfy both the inequalities 3f + 4 < 5 (4 − f) and 4f − 7 ≥ 2f − 13.

12. Given that x ≤ p < y satisfies both the inequalities 10 − p ≤ 6 and 5p − (3p − 7) < 31. Find the values of x and y.

13. Given that k is an integer that satisfies both the inequalities k + 3 < 7 and

3(7k − 2) ≥ 16 + 8(2k + 1). Find all the values of k.

14. List all the integer values of m that satisfy both the inequalities 4m − 13 ≥ 3 (m − 1)

and 9 − ≥ 4.

15. If p < e ≤ r is the solution for the inequalities − e < 12 and 3e ≤ 15 − (e + 31), find

the values of p and r.

16. The inequalities 4k − 1 < 3k + 13 and 20 − (3 − 2k) > 25 have the solution a < k < b. Find the values of a and b.

17. Solve the inequality h − 6 ≤ 2 (3 − h) < 8.

18. Given that y is an integer that satisfies the inequalities 17 − 5y ≥ 2 and 4 − 7(y + 2) < 11. Find all the values of y.

19. Determine the solution for both the inequalities 4 − 3c < 6 − c and 6c + 13 ≤ 4c + 31.

20. List all the integer values of r that satisfy both the inequalities + 3 > 4 and

3 (r + 5) − 14 ≤ 28.

© Pearson Malaysia Sdn. Bhd. 2008 Essential Mathematics PMR3