Answer: A. x -1 → -3x > -6. Dividing by -3 reverses the inequality: x < 2.

Chapter Exam

Chapter-5 Linear Inequalities — Online MCQ Test

Q: Which of the following is an example of a strict inequality?

Answer: B. x > 5 — A strict inequality uses symbols > or 5 is a strict inequality as it does not include the endpoint.

Q: What is a slack inequality also known as?

Answer: B. Non-strict inequality — Slack inequality (using ≥ or ≤) is also called non-strict inequality because it includes equality along with the inequality.

Q: On a number line, how is the solution to x > 3 represented?

Answer: B. Empty circle at 3 with arrow to the right — For strict inequality x > 3, an empty (unfilled) circle is used at 3 to show 3 is NOT included, with an arrow extending to the right.

Q: Solve: 2x + 3 < 9

Answer: A. x < 3 — 2x + 3 < 9 → 2x < 6 → x < 3. Subtracting 3 and dividing by 2 gives x < 3.

Q: What happens to an inequality symbol when both sides are multiplied by a negative number?

Answer: B. It reverses direction — When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed to maintain the truth of the statement.

Q: Solve the compound inequality: -1 ≤ 2x + 3 ≤ 7

Answer: A. -2 ≤ x ≤ 2 — -1 ≤ 2x + 3 ≤ 7 → subtract 3 from all parts: -4 ≤ 2x ≤ 4 → divide by 2: -2 ≤ x ≤ 2.

Q: Solve: |x - 3| < 2 and express in interval notation.

Answer: A. (1, 5) — |x - 3| < 2 means -2 < x - 3 < 2, which gives 1 < x < 5 or (1, 5) in interval notation.

Q: What is the solution set for the inequality: (x - 2)(x + 3) > 0 considering only linear analysis boundaries?

Answer: C. Cannot determine from linear methods alone — While this appears to be a product, solving (x - 2)(x + 3) > 0 requires quadratic analysis (sign analysis), not linear methods covered in Grade 11 linear inequalities chapter.

MATHS · Grade 11 · CBSE(NCERT)

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Chapter-5 Linear Inequalities — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 11 MATHS — Chapter-5 Linear Inequalities, with answers and explanations. These are sample questions; the exam has its own separate question set.

Which of the following is an example of a strict inequality?

A. x ≥ 5
B. x > 5 ✓
C. x ≤ 5
D. x = 5

Answer: B. x > 5
A strict inequality uses symbols > or < without equality. x > 5 is a strict inequality as it does not include the endpoint.

What is a slack inequality also known as?

A. Strict inequality
B. Non-strict inequality ✓
C. Equation
D. Linear equation

Answer: B. Non-strict inequality
Slack inequality (using ≥ or ≤) is also called non-strict inequality because it includes equality along with the inequality.

On a number line, how is the solution to x > 3 represented?

A. Filled circle at 3 with arrow to the right
B. Empty circle at 3 with arrow to the right ✓
C. Filled circle at 3 with arrow to the left
D. Empty circle at 3 with arrow to the left

Answer: B. Empty circle at 3 with arrow to the right
For strict inequality x > 3, an empty (unfilled) circle is used at 3 to show 3 is NOT included, with an arrow extending to the right.

Solve: 2x + 3 < 9

A. x < 3 ✓
B. x > 3
C. x ≤ 3
D. x ≥ 3

Answer: A. x < 3
2x + 3 < 9 → 2x < 6 → x < 3. Subtracting 3 and dividing by 2 gives x < 3.

Solve: 5 - 3x > -1

A. x < 2 ✓
B. x > 2
C. x ≤ 2
D. x ≥ 2

Answer: A. x < 2
5 - 3x > -1 → -3x > -6. Dividing by -3 reverses the inequality: x < 2.

What happens to an inequality symbol when both sides are multiplied by a negative number?

A. It remains the same
B. It reverses direction ✓
C. It becomes an equation
D. It becomes undefined

Answer: B. It reverses direction
When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed to maintain the truth of the statement.

Solve the compound inequality: -1 ≤ 2x + 3 ≤ 7

A. -2 ≤ x ≤ 2 ✓
B. -1 ≤ x ≤ 2
C. -2 ≤ x ≤ 1
D. -3 ≤ x ≤ 1

Answer: A. -2 ≤ x ≤ 2
-1 ≤ 2x + 3 ≤ 7 → subtract 3 from all parts: -4 ≤ 2x ≤ 4 → divide by 2: -2 ≤ x ≤ 2.

Solve: |x - 3| < 2 and express in interval notation.

A. (1, 5) ✓
B. [1, 5]
C. (1, 3)
D. (3, 5)

Answer: A. (1, 5)
|x - 3| < 2 means -2 < x - 3 < 2, which gives 1 < x < 5 or (1, 5) in interval notation.

What is the solution set for the inequality: (x - 2)(x + 3) > 0 considering only linear analysis boundaries?

A. Only between -3 and 2
B. x < -3 or x > 2 (considering quadratic nature)
C. Cannot determine from linear methods alone ✓
D. x > -3

Answer: C. Cannot determine from linear methods alone
While this appears to be a product, solving (x - 2)(x + 3) > 0 requires quadratic analysis (sign analysis), not linear methods covered in Grade 11 linear inequalities chapter.

A student claims that if x < 5 then x² < 25. Which evaluation is correct?

A. The claim is always true
B. The claim is always false
C. The claim is sometimes true and sometimes false (e.g., x = -6 gives x² = 36 > 25) ✓
D. Cannot be determined without additional information

Answer: C. The claim is sometimes true and sometimes false (e.g., x = -6 gives x² = 36 > 25)
For x < 5: if 0 < x < 5, then x² < 25 is true; but if x < 0 (say x = -6), then x² = 36 > 25, making the claim false. Squaring non-linear operations don't preserve inequality direction for all real numbers.

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