Practice the questions given in the worksheet on laws of inequality.
1. State true or false.
(i) x < - y ⟹ -x > y
(ii) -5x ≥ 15 ⟹ x ≥ -3
(iii) 2x ≤ -7 ⟹ \(\frac{2x}{-4}\) ≥ \(\frac{-7}{-4}\)
(iv) 7 > 5 ⟹ \(\frac{1}{7}\) < \(\frac{1}{5}\)
2. If x ≥ -y then mark each of the following sentences as true or false.
(i) - x ≥ -y
(ii) x + 2 ≤ y + 3
(iii) \(\frac{x}{3}\) ≤ \(\frac{y}{3}\)
(iv) ax ≥ ay, where a < 0
3. State, whether the following statements
are true or false.
(i) If ax + b > c then ax > c - b
(ii) If ax + b > c then x < \(\frac{c - b}{a}\), where a is a negative number.
(iii) If a > b then a + c > b + c
(iv) If a > b then a - c > b - c
(v) If a < b, then a - c < b - c
(vi) If a < b then ac < bc, c ≠ 0.
(vii) If a < b, then ac > bc
(viii) If a > b then \(\frac{a}{c}\) > \(\frac{b}{c}\), c ≠ 0.
(ix) If a - c < b - d then a + d < b + c.
(x) If a < b, and c > 0, then a - c > b - c, where a, b, c and d are real numbers and c ≠ 0.
4. If x > -5, find the least positive and negative integral values of x.
5. (i) If (x - 2)(x - 5) < 0 and x ∈ N then find x.
(ii) If (x + 3)(2 - x) > 0 and x ∈ Z then find x.
6. If 5 – 2x ≥ 1, what is the maximum value of x?
7. If x > y and z < 0, which of the following is correct?
(i) xz > yz
(ii) xz < yz
Answers for the worksheet on laws of inequality are given below:
Answers:
1. (i) True
(ii) False
(iii) True
(iv) True
2. True
(i) True
(ii) True
(iii) True
(iv) True
3. (i) True
(ii) True
(iii) True
(iv) True
(v) True
(vi) False (when c < 0)
(vii) False
(viii) False (when c < 0)
(ix) True
(x) False
4. Least positive number = 1, least negative number = -4
5. (i) 3, 4
(ii) -2, -1, 0, 1
6. 2
7. xz < yz
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