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 = \(\frac{11}{3}\)
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