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:
Answers:
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 = \(\frac{11}{3}\)
From Worksheet on Solution of a Linear Inequation in One Variable to HOME
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.