Class 11 Maths Chapter 5 Linear Inequalities – Extra Questions with Answers

Extra practice questions for Class 11 Maths Chapter 5 (Linear Inequalities), beyond the textbook. These Class 11 Maths Chapter 5 important questions are handy for last-minute exam practice.

Very Short Answer Questions (1 mark)

Q1. Solve for x: x + 3 > 7.
Ans: x > 4.

Q2. Solve for x: −2x < 8.
Ans: x > −4 (direction reversed since divided by negative).

Q3. Should the boundary line be solid or dashed for the inequality y < 2x+1?
Ans: Dashed (strict inequality, boundary excluded).

Q4. Is x = 5 included in the solution set of x ≥ 5?
Ans: Yes.

Q5. What symbol represents “at most”?
Ans: ≤.

Short Answer Questions (2–3 marks)

Q6. Solve the inequality 3x − 5 ≤ 2x + 1, showing all steps.
Ans: 3x − 2x ≤ 1 + 5, giving x ≤ 6.

Q7. Solve and represent on a number line: −3 < 2x + 1 ≤ 5.
Ans: Subtract 1 throughout: −4 < 2x ≤ 4. Divide by 2: −2 < x ≤ 2. On the number line: open circle at −2, closed (filled) circle at 2, shaded between.

Q8. A test point method is used to shade the region for x + y ≤ 4. Using the origin (0,0) as the test point, determine which side of the line x+y=4 should be shaded.
Ans: Substituting (0,0): 0+0 = 0 ≤ 4, which is TRUE, so the origin satisfies the inequality, meaning the side of the line containing the origin should be shaded.

Higher-Order Thinking / Application Questions

Q9. A factory produces two products, A and B. Constraints require 2x + 3y ≤ 12 (resource limit) and x, y ≥ 0 (non-negative production). Sketch (describe in words) the feasible region, and identify one point that satisfies all constraints.
Ans: The feasible region is a triangle bounded by the x-axis, y-axis, and the line 2x+3y=12 (with the region including the origin side, since (0,0) satisfies 2(0)+3(0)=0≤12). One valid point satisfying all constraints: (2,2), since 2(2)+3(2)=4+6=10≤12, and both x=2, y=2 are non-negative.

Q10. Explain, using an example, why the rule “reverse the inequality when multiplying/dividing by a negative” is necessary, rather than just an arbitrary rule to memorise.
Ans: Consider 2 < 3 (a true statement). Multiplying both sides by −1 without reversing would give −2 < −3, which is FALSE (−2 is actually greater than −3). Reversing the inequality gives −2 > −3, which is TRUE. This shows the rule isn’t arbitrary — it’s necessary to keep the inequality mathematically consistent, since multiplying by a negative number flips the relative order of numbers on the number line.

Written by Satish

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