Class 11 Maths · Original EZT practice
Linear Inequalities (Class 11 Chapter 5): summary and practice
Linear inequalities swap the equals sign for <, >, <= or >=, and the answer becomes a whole range of numbers instead of one value. The rules mirror equation-solving, with one famous twist: multiply or divide by a negative number and the sign flips. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 21 October 2026:
1. What an inequality is
Two expressions joined by <, >, <= or >= form an inequality. Strict inequalities use < or >; slack ones use <= or >=. The chapter opens with real situations, like 30x < 200 for rice packets bought with a fixed budget, where an equation cannot capture 'at most'.
2. The solving rules
You may add or subtract the same number on both sides freely. You may multiply or divide by a positive number freely. But multiplying or dividing by a negative number reverses the sign - < becomes > and vice versa.
3. Number-line graphs
Solutions are ranges, so they are drawn on the number line: an open circle at the endpoint for a strict inequality, a dark (closed) circle when the endpoint is included, and a bold line over every x that works.
4. Systems of one-variable inequalities
A system asks for x satisfying two inequalities at once - solve each, then keep only the overlap on the number line. The reprint defines two-variable forms like ax + by < c, but every solved system in this chapter stays in one variable.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Solve a basic inequality
Choose the method: Move constants across exactly as in equations.
EZT practice question
Solve 3x - 5 < 7 and show the solution on the number line.
Show the worked solution
- Add 5 to both sides: 3x < 12.
- Divide by 3 (positive, sign stays): x < 4.
- Graph: open circle at 4, bold line to the left.
Answer: x < 4.
Check: Test x = 0: -5 < 7 holds; test x = 5: 10 < 7 fails - the boundary sits at 4.
Watch for this: The answer is a range, not one number - report x < 4, never just 4.
Now try it yourself
Solve 5x + 2 > 17.
Check your answer
x > 3.
5x > 15, then divide by 5: x > 3.
Handle <= and >=
Choose the method: Same steps; the endpoint joins the solution set.
EZT practice question
Solve 2x + 3 >= 11.
Show the worked solution
- Subtract 3: 2x >= 8.
- Divide by 2: x >= 4.
- Graph: closed (dark) circle at 4, bold line to the right.
Answer: x >= 4.
Check: x = 4 gives 11 >= 11, which is true - the endpoint belongs.
Watch for this: Do not draw an open circle for a slack inequality - 4 itself is a solution here.
Now try it yourself
Solve 4x - 1 <= 15.
Check your answer
x <= 4.
4x <= 16, then divide by 4: x <= 4.
Reverse the sign on a negative step
Choose the method: Multiplying or dividing by a negative number flips the inequality.
EZT practice question
Solve -2x > 6.
Show the worked solution
- Divide both sides by -2.
- Because -2 is negative, > flips to <.
- x < -3. Graph: open circle at -3, bold line leftwards.
Answer: x < -3.
Check: Test x = -4: -2 x (-4) = 8 > 6 holds; test x = 0: 0 > 6 fails.
Watch for this: Forgetting the flip is the chapter's biggest error - -2x > 6 does NOT give x > -3.
Now try it yourself
Solve -3x <= 12.
Check your answer
x >= -4.
Divide by -3 and flip: x >= -4.
Translate a statement problem
Choose the method: Let x be the unknown, then write the budget or limit as an inequality.
EZT practice question
Rice costs 30 rupees a packet and Ravi has 200 rupees. Write and solve the inequality for the number of packets x he can buy.
Show the worked solution
- Total spent is 30x, and it cannot exceed 200: 30x < 200 (the chapter's own opening situation).
- Divide by 30: x < 6.67 (approximately).
- Packets come whole, so x can be at most 6.
Answer: 30x < 200, so x < 6.67 - Ravi can buy at most 6 packets.
Check: 6 packets cost 180 rupees; 7 would cost 210, over budget.
Watch for this: A statement problem ends in words: give the whole-number answer, not just the inequality's solution.
Now try it yourself
Pens cost 20 rupees each and Meena has 100 rupees. How many can she buy?
Check your answer
At most 5 pens.
20x <= 100 gives x <= 5.
Solve a double inequality
Choose the method: Apply every step to all three parts at once.
EZT practice question
Solve 3 < 2x - 1 <= 9.
Show the worked solution
- Add 1 throughout: 4 < 2x <= 10.
- Divide by 2 throughout: 2 < x <= 5.
- Graph: open circle at 2, closed circle at 5, bold line between.
Answer: 2 < x <= 5.
Check: Test x = 3: 3 < 5 <= 9 holds. Test x = 2: 3 < 3 fails, so 2 is excluded - as the open circle says.
Watch for this: One-sided steps break the chain - whatever you add or divide, do it to all three parts.
Now try it yourself
Solve 1 <= x - 2 < 4.
Check your answer
3 <= x < 6.
Add 2 throughout: 3 <= x < 6.
Solve a system in one variable
Choose the method: Solve each inequality, then keep the overlap.
EZT practice question
Solve the system: 2x - 3 < 7 and 9 - 4x <= 1. Show the common solution on the number line.
Show the worked solution
- First: 2x < 10, so x < 5.
- Second: -4x <= -8, and dividing by -4 flips the sign, so x >= 2.
- Overlap of x < 5 and x >= 2 is 2 <= x < 5 - bold line from closed 2 to open 5.
Answer: 2 <= x < 5.
Check: Test x = 3: 3 < 7 true and -3 <= 1 true. Test x = 6: first inequality fails, so 6 is out.
Watch for this: A system needs BOTH inequalities at once - keep only the common stretch of the number line.
Now try it yourself
Solve the system: x - 1 > 0 and 3x < 12.
Check your answer
1 < x < 4.
x > 1 and x < 4 overlap as 1 < x < 4.
Try a mixed set
Choose a method or explanation before opening each answer.
1. What happens when you multiply by a negative number?
Show answer and reason
The inequality sign reverses.
Negating swaps which side is larger.
2. Open circle or closed circle for x < 4?
Show answer and reason
Open circle at 4.
4 itself is not a solution under a strict sign.
3. Closed circle when?
Show answer and reason
For <= or >=, where the endpoint is included.
The endpoint satisfies the equality part.
4. Solution of an inequality - one number?
Show answer and reason
No, a whole range of numbers.
That is why we draw solution sets on the number line.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Solve 5x + 2 > 17.
- Solve -3x <= 12.
- Solve 1 <= x - 2 < 4.
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Questions about this practice page
- How is an inequality different from an equation?
- An equation pins x to one value (or a few); an inequality describes a whole range, like x < 4. The solving steps look similar, but the answer is a set of numbers drawn on the number line.
- Why does the sign reverse when multiplying by a negative?
- Negating two numbers swaps their order: 2 < 3, but -2 > -3. So any multiplication or division by a negative number must flip the inequality sign to stay true.
- How do I graph x >= 4 on the number line?
- Put a closed (dark) circle at 4 - the endpoint is included - and draw a bold line to the right over every x greater than 4.
- Does this chapter cover linear inequalities in two variables?
- The Reprint 2026-27 chapter defines two-variable forms like ax + by < c in section 5.2, but its solved content and exercise stay with one variable and number-line graphs - no two-variable systems are solved in this chapter PDF.
- Are these the NCERT exercise questions for Linear Inequalities (Class 11)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.