# Worksheet on Solution of a Linear Inequation in One Variable

Practice the questions given in the worksheet on solution of a linear inequation in one variable

1. If x ∈ N, find the solution set of the linear inequations.

(i) 5x + 3 ≤ 2x + 18

(ii) 3x - 2 < 19 - 4x

2. (i) Is x = -2 a solution of inequation 4x + 3 < 3x - 1? Why?

(ii) Is x = 1 a solution of inequation 2x + 1 ≥ x - 3? Why?

3. Solve the inequation: 3 - 2x ≥ x - 12 given that x ∈ N.

4. Solve the inequations in R:

(i) x – 2 > 3

(ii) 2x < 10

(iii) -3x ≥ -12

(iv) 4x - 3 ≥ 9

(v) 5 - 2x < 115.

5. If 25 - 4x ≤ 16, find:

(i) the smallest value of x, when x is a real number,

(ii) The smallest value of x, when x is an integer.

6. x is a positive integer satisfying 30 - 4(2x + 1) < 30. Find the solution set of the inequation.

7. Solve the inequations in R:

(i) -x + 7 > 4x - 3

(ii) 7x - 5x ≥ 3 + x

(iii) 2(x + 1) ≤ x + 5

(iv) 5(3x - 2) < 3(4x - 3)

(v) 3 + $$\frac{x}{4}$$ > $$\frac{x}{5}$$ + 7

(vi) $$\frac{x - 1}{7}$$ ≥ $$\frac{x + 3}{3}$$

8. If x and y be positive integers satisfying x + y ≤ 2. What are the possible values of x and y?

9. Find the largest value of x for which 2(x - 1) ≤ 9 - x and x ∈ W

10. Solve the inequations:

(i) 3 + 5x > 3x - 3, where x is a negative integer

(ii) 5x + 4 < 2x + 19, where x ∈ N.

(iii) $$\frac{x}{2}$$ + 2 ≤ $$\frac{x}{3}$$ + 3, where x is a positive odd integer.

(iv) 2x + 3 ≥ x + 5, where x is a natural number less than 4.

(v) $$\frac{x + 3}{3}$$ ≤ $$\frac{x + 8}{4}$$, where x is positive even integer.

(vi) $$\frac{3}{5}$$x - $$\frac{2}{3}$$(x - 2) > 1, where x ∈ {2, 4, 6, 8, 10}

11. Solve the inequation: 12 + 1$$\frac{5}{6}$$x  ≤ 5 + 3x and x ∈ R

12. (i) Find the smallest value of x for which 3 + $$\frac{5}{3}$$x < 2x + $$\frac{7}{2}$$, where x ∈ Z.

(ii) Find the general value of x for which x - 1 ≤ $$\frac{9 - x}{2}$$, where x ∈ R

Answers for the worksheet on solution of a linear inequation in one variable are given below:

1. (i) {1, 2, 3, 4, 5}

(ii) {1, 2}

2. (i) No, because -5 < -7 is not true.

(ii) Yes, 3 ≥ -2 is true.

3. {1, 2, 3, 4, 5}

4. (i) x > 5

(ii) x < 5

(iii) x ≤ 4

(iv) x ≥ 3

(v) x > - 3

5. (i) 2.25

(ii) 3

6. {1, 2, 3, ........}

7. (i) x < 2

(ii) x ≥ 3

(iii) x ≤ 3

(iv) x < $$\frac{1}{3}$$

(v) x > 80

(vi) x ≤ -6

8. x = 1, y = 1

9. 3

10. (i) x = -2, -1

(ii) x = 1, 2, 3, 4

(iii) x = 1, 3, 5

(iv) x = 2, 3

(v)x = 2, 4, 6, 8, 10, 12

(vi) x = 2, 4

11. {x : x ∈ R and x ≥ 6}

12. (i) x = -1

(ii) x = $$\frac{11}{3}$$

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