Linear Inequations Class 10 Selina Concise Exe-4A Replacement and Solution Set ISC Maths. In this article you would learn how to solve questions / Problems / example on Replacement and Solution Set in Linear Inequations with answer. Visit official website CISCE for detail information about ICSE Board Class-10 Mathematics.
Linear Inequations Class 10 Selina Concise Exe-4A Replacement and Solution Set ISC Maths
| Board | ICSE |
| Publications | Selina |
| Subject | Maths |
| Class | 10th |
| Chapter-4 | Linear Inequations (In one variable) |
| Writer | R.K. Bansal |
| Exe-4A | Replacement Set and Solution Set. |
| Edition | 2025-2026 |
Replacement and Solution Set Questions with Solutions
Linear Inequations Class 10 Selina Concise Exe-4A Replacement and Solution Set ISC Maths
Que-1: State, true or false :
(i) 𝑥 < −𝑦 ⇒ −𝑥 > 𝑦
(ii) −5𝑥 ≥15 ⇒𝑥 ≥ −3
(iii) 2𝑥 ≤−7 ⇒ 2𝑥/−4 ≥ −7/−4
(iv) 7 > 5 ⇒ 1/7 < 1/5
Sol: (i) True
(ii) false
Explanation :
-5x ≥ 15 = -15x/5 ≥ 15/5
x ≤ -3.
(iii) True
(iv) True
Que-2: State whether the following statements are true or false:
(i) If a < b, then a – c < b – c
(ii) If a > b, then a + c > b + c
(iii) If a < b, then ac > bc.
(iv) If a > b, then a/c < b/c
(v) If a – c > b – d; then a + d > b + c
(vi) If a < b, and c > 0, then a – c > b – c where a, b, c and d are real numbers and c ≠ 0.
Sol: (i) True
(ii) True
(iii) False
(iv) False
(v) True
(vi) False
Que-3: If x ∈ N, find the solution set of inequations.
(i) 5x + 3 ≤ 2x + 18
(ii) If x ∈ N, find the solution set of inequations.
Sol: (i) 5x + 3 ≤ 2x + 18
5x – 2x ≤ 18 – 3
3x ≤ 15
x ≤ 5
Since, x ∈ N, therefore solution set is {1, 2, 3, 4, 5}.
(ii) 3x – 2 < 19 – 4x
3x + 4x < 19 + 2
7x < 21
x < 3
Since, x ∈ N, therefore solution set is {1, 2}.
Que-4: If the replacement set is the set of whole numbers, solve:
(i) x + 7 ≤ 11
(ii) 3x – 1 > 8
(iii) 8 – x > 5
(iv) 7 −3𝑥 ≥ -1/2
(v) x−3/2 < 3/2-x
(vi) 18 ≤ 3x – 2
Sol: (i) x + 7 ≤ 11
x ≤ 11 – 7
x ≤ 4
Since, the replacement set = W …(Set of whole numbers)
⇒ Solution set = {0, 1, 2, 3, 4}
(ii) 3x – 1 > 8
3x > 8 + 1
x > 3
Since, the replacement set = W …(Set of whole numbers)
⇒ Solution set = {4, 5, 6, …}
(iii) 8 – x > 5
– x > 5 – 8
– x > – 3
x < 3
Since, the replacement set = W …(Set of whole numbers)
⇒ Solution set = {0, 1, 2}
(iv) 7 −3𝑥 ≥ −1/2
−3𝑥 ≥ −1/2 −7
−3𝑥 ≥ −15/2
𝑥 ≤ 5/2
Since, the replacement set = W …(Set of whole numbers)
∴ Solution set = {0, 1, 2}
(v) 𝑥 − (3/2) < (3/2) − 𝑥
𝑥 + 𝑥 < (3/2) + (3/2)
2x < 3
𝑥 < 3/2
Since, the replacement set = W …(Set of whole numbers)
∴ Solution set = {0, 1}
(vi) 18 ≤ 3x – 2
18 + 2 ≤ 3x
20 ≤ 3x
𝑥 ≥ 20/3
Since, the replacement set = W …(Set of whole numbers)
∴ Solution set = {7, 8, 9, …}
Que-5: Solve the inequation:
3 – 2x ≥ x – 12 given that x ∈ N.
Sol: 3 – 2x ≥ x – 12
–2x – x ≥ –12 – 3
–3x ≥ –15
x ≤ 5
Since, x ∈ N, therefore,
Solution set = {1, 2, 3, 4, 5}
Que-6: 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.
Sol: 25 – 4x ≤ 16
– 4x ≤ 16 – 25
– 4x ≤ – 9
𝑥 ≥ 9/4
x ≥ 2.25
The smallest integer greater than or equal to 2.25 is 3
(i) The smallest value of x, when x is a real number, is 2.25.
(ii) The smallest value of x, when x is an integer, is 3.
Que-7: If the replacement set is the set of real numbers, solve:
(i) – 4x ≥ – 16 (ii) 8 – 3x ≤ 20 (iii) 5 + (x/4) > (x/5) + 9 (iv) (x+3)/8 < (x-3)/5
Sol: (i) – 4x ≥ – 16
4x ≤ 16
𝑥 ≤ 16/4
x < 4
Since the replacement set of real numbers
∴ Solution set = {x : x ∈ R and x ≤ 4}
(ii) 8 – 3x ≤ 20
– 3x ≤ 20 – 8
– 3x ≤ 12
3x ≥ – 12
𝑥 ≥ −12/3
x ≥ – 4
Since the replacement set of real numbers.
∴ Solution set = {x : x ∈ R and x ≥ – 4}
(iii) 5 + (𝑥/4) > (𝑥/5) + 9
(𝑥/4) − (𝑥/5) > 9 −5
(𝑥/20) >4
x > 80
Since the replacement set of real numbers.
∴ Solution set = {x : x ∈ R and x > 80}
(iv) (𝑥+3)/8 < (𝑥−3)/5
5x + 15 < 8x – 24
5x – 8x < –24 – 15
–3x < –39
x > 13
Since the replacement set of real numbers.
∴ Solution set = {x : x ∈ R and x > 13}
Que-8: Find the smallest value of x for which 5 − 2𝑥 < {5*(1/2)} − (5x/3), where x is an integer.
Sol: 5 −2𝑥 < {5*(1/2)} − (5x/3)
−2𝑥 + (5x/3) < (11/2) − 5
−𝑥/3 < 1/2
−𝑥 < 3/2
𝑥 > −3/2
x > –1.5
Thus, the required smallest value of x is –1.
Que-9: Find the largest value of x for which 2(x – 1) ≤ 9 – x and x ∈ W.
Sol: 2(x – 1) ≤ 9 – x
2x – 2 ≤ 9 – x
2x + x ≤ 9 + 2
3x ≤ 11
𝑥 ≤11/3
x ≤ 3.66
Since, x ∈ W, thus the required largest value of x is 3.
Que-10: Solve the inequation:
12 + {1*(5x/6)} ≤ 5 +3𝑥 and 𝑥 ∈ 𝑅.
Sol: 12 + {1*(5x/6} ≤ 5 +3𝑥
(11x/6) −3𝑥 ≤ 5 −12
(11𝑥−18𝑥)/6 ≤ −7
−7𝑥/6 ≤ −7
𝑥 ≥ (7×6)/7
𝑥 ≥ 6
∴ Solution set = {x : x ∈ R and x ≥ 6}
Que-11: Given x ∈ {integers}, find the solution set of:
–5 ≤ 2x – 3 < x + 2
Sol: –5 ≤ 2x – 3 < x + 2
⇒ –5 ≤ 2x – 3 and 2x – 3 < x + 2
⇒ –5 + 3 ≤ 2x and 2x – x < 2 + 3
⇒ –2 ≤ 2x and x < 5
⇒ x ≥ –1 and x < 5
Since x ∈ {integers}
∴ Solution set = {–1, 0, 1, 2, 3, 4}
Que-12: Given x ∈ {whole numbers}, find the solution set of:
–1 ≤ 3 + 4x < 23
Sol: –1 ≤ 3 + 4x < 23
⇒ –1 ≤ 3 + 4x and 3 + 4x < 23
⇒ – 4 ≤ 4x and 4x < 20
⇒ x ≥ –1 and x < 5
Since, x in {whole numbers}
∴ Solution set = {0, 1, 2, 3, 4}
–: End of Linear Inequations Class 10 Selina Concise Exe-4A Replacement and Solution :–
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