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Chapter 5 · Class XI Mathematics · MCQ Practice

MCQ Practice Arena

Linear Inequalities

Solve Faster, Score Higher — Master the Sign-Flip Rule

📋 50 MCQs ⭐ 0 PYQs ⏱ 75 sec/Q

🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs

10Easy

18Medium

22Hard

0PYQs

75 secAvg Time/Q

4Topics

Easy 20% Medium 36% Hard 44%

Why Practise These MCQs?

JEE MainCBSEBITSAT

Linear Inequalities MCQs are among the fastest to solve — most take under 60 seconds. JEE Main asks 1–2 questions on solution sets and modulus inequalities. CBSE objective section tests graphical representation. BITSAT includes systems of inequalities. This chapter is a reliable marks-saver.

Topic-wise MCQ Breakdown

One-Variable Inequalities34 Q

Compound Inequalities10 Q

Fractional Inequalities6 Q

Word Problems0 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\mathrm{Multiply/divide\ by\ negative\ →\ flip\ inequality}$

$|x| < a ⟺ −a < x < a$

$|x| > a ⟺ x < −a or x > a$

$\mathrm{a < x < b\ on\ number\ line:\ open\ interval\ (a,b)}$

MCQ Solving Strategy

The golden rule: whenever you multiply or divide both sides by a negative number, flip the inequality sign — this single rule causes 60% of errors. For |x| < a type MCQs, always split into −a < x < a immediately. For graphical two-variable questions, shade the correct half-plane by testing the origin.

⚠ Common Traps & Errors

⚠Forgetting to flip inequality when dividing by negative
⚠|x−2| < 3 gives −1 < x < 5, not −3 < x < 3
⚠Open vs closed circles on number line (< vs ≤)
⚠Origin test fails if origin lies on the boundary line

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Solve basic linear inequality, shade on number line

② Medium

Modulus inequalities, intersection of two solution sets

③ Hard

System of three inequalities, word problems with constraints

★ PYQ

JEE Main — solution set as interval; CBSE — graphical shading

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Permutations & Combinations MCQs

🎯 Knowledge Check

Maths — LINEAR INEQUALITIES

50 Questions Class 11 MCQs

Which of the following represents a linear inequality in one variable?
(Class XI – Basics)

a a. $2x + 3 = 7$ b b. $x^2 - 1 < 0$ c c. $3x - 5 > 0$ d d. $x^2 = 4$

Solve the inequality $x - 4 \le 0$.
(Class XI – Basics)

a a. $x \le 4$ b b. $x < 4$ c c. $x \ge 4$ d d. $x > 4$

The solution set of $2x > 6$ is:
(Class XI – Basics)

a a. $x > 2$ b b. $x < 3$ c c. $x > 3$ d d. $x \ge 3$

Which symbol represents “less than or equal to”?
(Class XI – Basics)

a a. $<$ b b. $>$ c c. $\le$ d d. $\ge$

If $x < 5$, then which of the following is a solution?
(Class XI – Basics)

a a. $6$ b b. $5$ c c. $4$ d d. $7$

Solve $3x + 1 \ge 7$.
(Class XI – Easy)

a a. $x \ge 1$ b b. $x \le 2$ c c. $x \ge 2$ d d. $x > 1$

Solve $5x - 10 < 0$.
(Class XI – Easy)

a a. $x < 2$ b b. $x > 2$ c c. $x \le 2$ d d. $x \ge 2$

The solution of $-2x > 6$ is:
(Class XI – Easy)

a a. $x > -3$ b b. $x < -3$ c c. $x > 3$ d d. $x < 3$

Solve $4 - x \le 1$.
(Class XI – Easy)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Which of the following is not a solution of $x \ge -1$?
(Class XI – Easy)

a a. $-1$ b b. $0$ c c. $2$ d d. $-2$

Solve the inequality $2( x - 3 ) > x + 1$.
(Class XI – Moderate)

a a. $x > 7$ b b. $x < 7$ c c. $x > 5$ d d. $x < 5$

The solution of $x + 5 < 2x - 1$ is:
(Class XI – Moderate)

a a. $x < 6$ b b. $x > 6$ c c. $x \le 6$ d d. $x \ge 6$

Solve $3x + 2 \le 2x + 5$.
(Class XI – Moderate)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $\dfrac{x}{2} > 3$.
(Class XI – Moderate)

a a. $x > 6$ b b. $x < 6$ c c. $x \ge 6$ d d. $x \le 6$

Which of the following satisfies $2x - 1 \ge 3$?
(Class XI – Moderate)

a a. $1$ b b. $2$ c c. $0$ d d. $-1$

Solve $\dfrac{3x - 1}{2} < 4$.
(Class XI – Moderate)

a a. $x < 3$ b b. $x < 5$ c c. $x > 3$ d d. $x > 5$

Solve $5 - 2x > 1$.
(Class XI – Moderate)

a a. $x < 2$ b b. $x > 2$ c c. $x \le 2$ d d. $x \ge 2$

Solve $7x - 3 \ge 4x + 6$.
(Class XI – Moderate)

a a. $x \ge 3$ b b. $x \le 3$ c c. $x > 3$ d d. $x < 3$

The solution of $-x + 4 \le 1$ is:
(Class XI – Moderate)

a a. $x \ge 3$ b b. $x \le 3$ c c. $x > 3$ d d. $x < 3$

Solve $2(3x + 1) \le 4x + 10$.
(Class XI – Moderate)

a a. $x \le 4$ b b. $x \ge 4$ c c. $x < 4$ d d. $x > 4$

Solve $1 < 2x + 3 \le 7$.
(Class XI – Higher)

a a. $-1 < x \le 2$ b b. $-1 \le x < 2$ c c. $-2 < x \le 2$ d d. $-1 < x < 2$

Solve $-3 \le x - 2 < 4$.
(Class XI – Higher)

a a. $-1 \le x < 6$ b b. $-5 \le x < 2$ c c. $-3 \le x < 4$ d d. $-1 < x \le 6$

Solve $2 \le 3x + 1 < 8$.
(Class XI – Higher)

a a. $\dfrac{1}{3} \le x < \dfrac{7}{3}$ b b. $1 \le x < 3$ c c. $\dfrac{2}{3} \le x < \dfrac{8}{3}$ d d. $\dfrac{1}{3} < x \le \dfrac{7}{3}$

Solve $-1 < \dfrac{x}{2} \le 3$.
(Class XI – Higher)

a a. $-2 < x \le 6$ b b. $-1 < x \le 3$ c c. $-2 \le x < 6$ d d. $-1 \le x < 3$

Solve $4x - 1 > 2x + 3$.
(Class XI – Higher)

a a. $x > 2$ b b. $x < 2$ c c. $x \ge 2$ d d. $x \le 2$

Solve $\dfrac{2x + 3}{5} \ge 1$.
(Class XI – Higher)

a a. $x \ge 1$ b b. $x > 1$ c c. $x \ge 2$ d d. $x > 2$

Solve $3 - 2x < 7 - x$.
(Class XI – Higher)

a a. $x < 4$ b b. $x > 4$ c c. $x \le 4$ d d. $x \ge 4$

Solve $-4x \le 8$.
(Class XI – Higher)

a a. $x \le -2$ b b. $x \ge -2$ c c. $x < -2$ d d. $x > -2$

If $x$ satisfies $2x - 5 \le 1$, then:
(Class XI – Higher)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $5x + 2 > 3x - 4$.
(Class XI – Higher)

a a. $x > -3$ b b. $x < -3$ c c. $x \ge -3$ d d. $x \le -3$

Solve $\dfrac{x - 1}{3} < 2$.
(Class XI – Advanced)

a a. $x < 7$ b b. $x > 7$ c c. $x \le 7$ d d. $x \ge 7$

Solve $2x + 1 \le 3(x - 1)$.
(Class XI – Advanced)

a a. $x \ge 4$ b b. $x \le 4$ c c. $x > 4$ d d. $x < 4$

Solve $-2 \le 5 - x < 4$.
(Class XI – Advanced)

a a. $1 < x \le 7$ b b. $1 \le x < 7$ c c. $-1 \le x < 5$ d d. $1 < x < 7$

Solve $3x - 7 > 2x + 5$.
(Class XI – Advanced)

a a. $x > 12$ b b. $x < 12$ c c. $x \ge 12$ d d. $x \le 12$

Solve $\dfrac{5 - x}{2} \ge 1$.
(Class XI – Advanced)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $x - 3 \le 2x + 1$.
(Class XI – Advanced)

a a. $x \ge -4$ b b. $x \le -4$ c c. $x > -4$ d d. $x < -4$

Solve $4( x - 2 ) < 2( x + 1 )$.
(Class XI – Advanced)

a a. $x < 5$ b b. $x > 5$ c c. $x \le 5$ d d. $x \ge 5$

Solve $-3x + 2 > -x - 4$.
(Class XI – Advanced)

a a. $x < 3$ b b. $x > 3$ c c. $x \le 3$ d d. $x \ge 3$

Solve $2 \le \dfrac{3x - 1}{2} < 5$.
(Class XI – Advanced)

a a. $\dfrac{5}{3} \le x < \dfrac{11}{3}$ b b. $1 \le x < 4$ c c. $\dfrac{3}{2} \le x < \dfrac{7}{2}$ d d. $\dfrac{5}{3} < x \le \dfrac{11}{3}$

Solve $-5 < 2 - x \le 1$.
(Class XI – Advanced)

a a. $1 \le x < 7$ b b. $1 < x \le 7$ c c. $-3 \le x < 4$ d d. $-3 < x \le 4$

Solve $\dfrac{2x - 3}{4} > \dfrac{x + 1}{2}$.
(Competitive – JEE Level)

a a. $x > 5$ b b. $x < 5$ c c. $x \ge 5$ d d. $x \le 5$

Solve $3 - \dfrac{x}{2} \le 1$.
(Competitive – JEE Level)

a a. $x \ge 4$ b b. $x \le 4$ c c. $x > 4$ d d. $x < 4$

Solve $5x + 1 > 2(2x + 3)$.
(Competitive – JEE Level)

a a. $x > 5$ b b. $x < 5$ c c. $x \ge 5$ d d. $x \le 5$

Solve $\dfrac{3x - 5}{2} \le \dfrac{x + 1}{4}$.
(Competitive – JEE Level)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $7 - 2x \ge 3x - 8$.
(Competitive – JEE Level)

a a. $x \le 3$ b b. $x \ge 3$ c c. $x < 3$ d d. $x > 3$

Solve $2(x + 1) > 3(x - 2)$.
(Competitive – JEE Level)

a a. $x < 8$ b b. $x > 8$ c c. $x \le 8$ d d. $x \ge 8$

Solve $-1 \le \dfrac{2x + 3}{3} < 3$.
(Competitive – JEE Level)

a a. $-3 \le x < 3$ b b. $-3 < x \le 3$ c c. $-6 \le x < 6$ d d. $-6 < x \le 6$

Solve $\dfrac{5 - 3x}{2} > \dfrac{1 - x}{4}$.
(Competitive – JEE Level)

a a. $x < 3$ b b. $x > 3$ c c. $x \le 3$ d d. $x \ge 3$

Solve $4x - 1 < 3( x + 2 )$.
(Competitive – JEE Level)

a a. $x < 7$ b b. $x > 7$ c c. $x \le 7$ d d. $x \ge 7$

Solve $-2 \le 3 - 2x < 4$.
(Competitive – JEE Level)

a a. $-\dfrac{1}{2} < x \le \dfrac{5}{2}$ b b. $-\dfrac{1}{2} \le x < \dfrac{5}{2}$ c c. $-\dfrac{5}{2} \le x < \dfrac{1}{2}$ d d. $-\dfrac{5}{2} < x \le \dfrac{1}{2}$

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Frequently Asked Questions

A linear inequality is an inequality of the form $ax + b < 0$, $ax + b \le 0$, $ax + b > 0$, or $ax + b \ge 0$, where $a$ and $b$ are real numbers and $a \ne 0$.

A linear equation uses an equality sign $=$ and has a unique solution, while a linear inequality uses $<, \le, >, \ge$ and has a range of solutions.

The symbols are less than $(<)$, less than or equal to $(\le)$, greater than $(>)$, and greater than or equal to $(\ge)$.

The solution set is the collection of all real numbers that satisfy the given inequality.

It is solved by isolating the variable using standard algebraic operations while maintaining the inequality sign.

The inequality sign is reversed when both sides are multiplied or divided by a negative number.

For $2x - 5 < 3$, we get $2x < 8$ and hence $x < 4$.

It is a graphical method where solutions are shown as points or intervals on the number line.

Strict inequalities $(<, >)$ are represented using open circles to exclude the boundary point.

Inclusive inequalities $(\le, \ge)$ are represented using closed circles to include the boundary point.

Compound linear inequalities involve two inequalities connected by “and” or “or”.

“And” means the intersection of solution sets, where both inequalities must be satisfied simultaneously.

“Or” means the union of solution sets, where at least one inequality must be satisfied.

For $1 < x < 5$, the solution is all real numbers between 1 and 5.

For $x < -2$ or $x > 3$, the solution includes numbers less than $-2$ and greater than $3$.

Linear Inequalities

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — LINEAR INEQUALITIES

Frequently Asked Questions

Recent Posts

LINEAR INEQUALITIES – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Practice Advance MCQs

Let's Connect

Linear Inequalities

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — LINEAR INEQUALITIES

Frequently Asked Questions

Q 01 What is a linear inequality?

Q 02 How does a linear inequality differ from a linear equation?

Q 03 What are the symbols used in linear inequalities?

Q 04 What is the solution set of a linear inequality?

Q 05 How is a linear inequality solved algebraically?

Q 06 What happens to the inequality sign when both sides are multiplied or divided by a negative number?

Q 07 Give an example of solving a simple linear inequality.

Q 08 What is meant by representation of linear inequalities on a number line?

Q 09 How are strict inequalities represented on a number line?

Q 10 How are inclusive inequalities represented on a number line?

Q 11 What are compound linear inequalities?

Q 12 What is meant by the word “and” in compound inequalities?

Q 13 What is meant by the word “or” in compound inequalities?

Q 14 Give an example of a compound inequality with “and”.

Q 15 Give an example of a compound inequality with “or”.

Recent Posts

LINEAR INEQUALITIES – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Practice Advance MCQs

Let's Connect