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CBSE · Class 11 · Mathematics

Linear Inequalities

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The solution of −6x − 2 < 1 is:
  1. x > −1/2
  2. x > 1/2
  3. x > 1/6
  4. x < −1/2
2.
The solution of 0 ≤ 6x + 8 < 17 is:
  1. −8 ≤ x < 9
  2. 4/3 ≤ x < 25/6
  3. −4/3 ≤ x < 3/2
  4. −4/3 < x ≤ 3/2
3.
How many integers x satisfy −12 ≤ 2x + 2 < 2?
  1. 9
  2. 8
  3. 6
  4. 7
4.
In interval notation, the solution of 6x ≥ −9 (x ∈ R) is:
  1. [−3/2, ∞)
  2. [3/2, ∞)
  3. (−∞, −3/2]
  4. (−3/2, ∞)
5.
When both sides of an inequality are multiplied by a negative number, the sign of the inequality:
  1. stays the same
  2. is reversed
  3. becomes =
  4. disappears
6.
The solution set of 7x + 1 < 14, when x is a natural number, is:
  1. {1}
  2. {2}
  3. φ
  4. {1, 2}
7.
A student scored 79, 61 in 2 tests. Can the student reach an average of at least 85 after one more test marked out of 100?
  1. No, it would need more than 100
  2. Only with a score of 0
  3. Yes, with 100
  4. Yes, with exactly the average so far
8.
Assertion (A): The solution of −8x < −13 is x < 13/8.
Reason (R): Multiplying or dividing both sides by a negative number reverses the inequality sign.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Solve: x/6 − 5 ≥ x/5 − 0.
10.
Solve 3 < 9 − 6x ≤ 12.
11.
Find all pairs of consecutive even positive integers, both greater than 11, whose sum is less than 43.
12.
Solve the system: 5x + 4 > 3 and 3x + 1 ≤ −2.
13.
A student's marks in two tests are 88 and 79, out of 100. What marks in the third test give an average between 65 and 80, inclusive?
14.
The temperature of a solution is kept between 20 °C and 60 °C. What is the range in degrees Fahrenheit? (F = 9C/5 + 32)
15.
Which of the points (1, 3), (5, −5), (−1, 0) satisfy 3x + 3y ≥ 4?
16.
List the integers x that satisfy −14 ≤ 5x − 5 ≤ 27.
Section C — Word problems4 × 4 = 16 marks
17.
A solution of 2,970 litres contains 60% acid. How many litres of water must be added so that the acid content is between 30% and 45%?
18.
Consider the system 2x + 4y ≤ 19, 4x − 3y ≥ −2, x ≥ 0, y ≥ 0. Which of the points (1, 3), (1, 2), (3, 3), (5, 6) lie in the solution region? Explain how you would shade the region.
19.
A company makes bags at a cost of Rs 1,000 plus Rs 100 per bag, and sells them at Rs 150 each. How many bags must it sell to make a profit of more than Rs 5,000?
20.
Solve each inequality and find the values of x that satisfy both: (i) (x − 3)/6 ≤ (x + 6)/2; (ii) 3x > −5.
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Mathematics

Answer key

Linear Inequalities · AW-11M-LIQ-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(a) x > −1/2−6x < 3; dividing by a negative number reverses the sign
2(c) −4/3 ≤ x < 3/2subtract 8, then divide by 6
3(d) 7−7 ≤ x < 0
4(a) [−3/2, ∞)x ≥ −3/2
5(b) is reversed—
6(a) {1}x < 13/7
7(a) No, it would need more than 100needs x ≥ 115
8(d) A is false, but R is true.A is false: divide by −8: x > 13/8. R is true.
9x ≤ −150multiply by 30: x(1/6 − 1/5) ≥ 5; the coefficient is negative, so the sign reverses
10−1/2 ≤ x < 1subtract 9, then divide by −6 and reverse both signs
11(12, 14), (14, 16), (16, 18), (18, 20), (20, 22)x > 11 and x + (x + 2) < 43, so x < 41/2
12no solutionx > −1/5 and x ≤ −1
13From 28 to 73195 ≤ 167 + x ≤ 240, and 0 ≤ x ≤ 100
14Between 68 °F and 140 °FF = 9C/5 + 32 at C = 20 and at C = 60
15(1, 3)(1, 3): 12; (5, −5): 0; (−1, 0): −3
16{−1, 0, 1, 2, 3, 4, 5, 6}−9/5 ≤ x ≤ 32/5
17Between 990 and 2,970 litres30 ≤ 60 × 2970 ÷ (2970 + x) ≤ 45
18(1, 2), (3, 3). Draw each boundary line as a solid line (≤, ≥), shade the side that contains a point satisfying it (test the origin where it is not on the line), and take the common region in the first quadrant.(1, 3): 14, −5; (1, 2): 10, −2; (3, 3): 18, 3; (5, 6): 34, 2
19More than 120 bags, so at least 121 bags150x − (1000 + 100x) > 5000
20(i) x ≥ −21/2; (ii) x > −5/3; both: x > −5/3(i) multiply by 12: 2(x − 3) ≤ 6(x + 6)