Click here to view solutions of Linear Inequations (MCQ)
Solutions of the MCQs of linear Inequations is given below
Solutions
Question:
Solution:
| Option (c) |
Question: If the replacement set is the set of whole
numbers (W), the solution set of the inequation 5x + 4 ≤ 24
- (a) {1, 2, 3, 4}
- (b) {……, −2, −1, 0, 1, 2, 3, 4}
- (c) {4, 5, 6}
- (d) {0, 1, 2, 3, 4}
Solution: 5x + 4 ≤ 24
⇒ 5x ≤ 20
⇒ x ≤ 4
Solution set {0, 1, 2, 3, 4}
| Option (d) |
Question: The smallest value of x of the inequation 25 − 4 x ≤ 16, X ∈ R
- (a) 2
- (b) (9/4)
- (c) 3
- (d) 2.75
Solution: 25 − 4 x ≤ 16, X ∈ R
⇒ − 4 x ≤ − 9
⇒ 4 x ≥ 9 ⇒ x ≥ (9/4)
Smallest value = (9/4)
| Option (b) |
Question: Identify the correct solution set of the following number line:
- (a) {x : x ∈ Z, −4 < x < 5}
- (b) {x : x ∈ Z, −4 ≤ x ≤ 5}
- (c) {x : x ∈ R, −4 ≤ x ≤ 5}
- (d) {x : x ∈ R, −4 < x < 5}
Solution: {x : x ∈ R, −4 ≤ x ≤ 5}
| Option (c) |
Question: The largest value of x for which
2(x −1) ≤ 9 − x and x ∈ W is
- (a) 4
- (b) (11/3)
- (c) 3
- (d) 0
Solutions: 2(x −1) ≤ 9 − x and x ∈ W is
⇒ 2x − 2 ≤ 9 − x
⇒ 3x ≤ 11
⇒ x ≤ (11/3)
⇒ x ≤ 3 + (2/3), x ∈ W
∴ the largest value of x is three.
| Option (c) |
Question: Choose the range of values of x for which both the following inequations are true
x > 2 & −1 ≤ x ≤ 5
- (a) 2 ≤ x ≤ 5
- (b) 2 < x < 5
- (c) 2 < x ≤ 5
- (d) 2 ≤ x < 5
Solutions: 2 < x ≤ 5
| Option (c) |
Question: If x is positive odd integer, the solution set of inequation
(x/2) + 5 ≤ (x/3) + 6
- (a) {1, 3, 5, 7}
- (b) {1, 2, 3, 4, 5}
- (c) {2, 4}
- (d) {1, 3, 5}
Solutions: (x/2) + 5 ≤ (x/3) +6
⇒ (x/2) − (x/3) ≤ 6 − 5
⇒ (x/6) ≤ 1
⇒ x ≤ 6
⇒ x = (1, 3, 5}
| Option (d) |
Question: The solution set of the following inequation is
2 ≤ 3x + 5 < 13 when x ∈ Z
- (a) {−1, 0, 1, 2, 3}
- (b) {0, 1, 2, 3}
- (c) {0, 1, 2}
- (d) {−1, 0, 1, 2}
Solution: 2 ≤ 3x + 5 < 13 when x ∈ Z
⇒ 2 − 5 ≤ 3x + 5 − 5 < 13 − 5
⇒ − 3 ≤ 3x < 8
⇒ − 1 ≤ x < (8/3)
Solution set = {−1, 0, 1, 2}
| Option (d) |
Question: The solution set of the inequation
7 x −4(3 −x) ≥ 3(2 x −5) when x ∈ {−3, −2, −1, 0, 1, 2, 3}
- (a) { 0, 1, 2, 3}
- (b) { −2, −1, 0, 1, 2, 3}
- (c) { 0, 1, 2}
- (d) {−3, −2, −1, 0, 1}
Solution: 7 x −4(3 −x) ≥ 3(2 x −5) when x ∈ {−3, −2, −1, 0, 1, 2, 3}
⇒ 7 x − 12 + 4 x ≥ 6 x − 15
⇒11 x − 12 ≥ 6 x − 15
⇒ 5 x ≥ − 3
⇒ x ≥ −(3/5)
Solution set = {0, 1, 2, 3}
| Option (a) |
Question: If the replacement set is the set of real numbers, the solution set of the inequation
- (a) {x : x ∈ R; x > 13}
- (b) {x : x ∈ R; x < 13}
- (c) { x : x ∈ R; x ≥ 13}
- (d) { x : x ∈ R; x ≤ 13}
Solution:
⇒ (x + 3) 5 < (x − 3) 8
⇒ 5 x + 15 < 8x − 24
⇒ 5 x − 8 x < −24 − 15
⇒ − 3 x < − 39
⇒ 3 x > 39
⇒ x > 13
Solution set = {x : x ∈ R; x > 13}
| Option (a) |
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