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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