Class 11 • Maths • Chapter 5
LINEAR INEQUALITIES
True & False Quiz
Bound it. Graph it. Solve it.
✓True
✗False
25
Questions
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Ch.5
Chapter
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XI
Class
Why True & False for LINEAR INEQUALITIES?
How this format sharpens your conceptual clarity
🔵 Inequalities model real-world constraints — profit margins, temperature ranges, and optimisation.
✅ T/F reveals the CRITICAL rule: multiplying or dividing by a negative number REVERSES the inequality sign.
🎯 Graphing solution sets on a number line — open vs closed intervals — is a common CBSE trap.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
A linear inequality in one variable can be represented on a number line.
Q 2
The solution of the inequality \(x<3\) includes the number \(3\).
Q 3
If \(x>5\), then every number greater than \(5\) satisfies the inequality.
Q 4
The inequality \(x\le 0\) has infinitely many solutions.
Q 5
The graph of \(x\ge -2\) on the number line uses a filled circle at \(-2\).
Q 6
Adding the same real number to both sides of an inequality does not change its solution set.
Q 7
Subtracting a number from both sides of an inequality may reverse the inequality sign.
Q 8
Multiplying both sides of an inequality by a positive number keeps the inequality sign unchanged.
Q 9
Multiplying both sides of an inequality by a negative number keeps the inequality sign unchanged.
Q 10
The solution of \(2x-4>0\) is \(x>2\).
Q 11
The inequality \(3x+1\le 7\) has the solution \(x\le 2\).
Q 12
The solution set of \(x^2<4\) is \(-2<x<2\).
Q 13
The inequality \(x^2>9\) is satisfied by all \(x>3\) and \(x<-3\).
Q 14
A system of linear inequalities in one variable always has a unique solution.
Q 15
The solution of \(x>1\) and \(x<1\) is the empty set.
Q 16
The inequality \(\frac{x-1}{2}>3\) has the solution \(x>7\).
Q 17
The inequality \(\frac{x-1}{-2}>3\) has the solution \(x> -5\).
Q 18
The solution set of \(|x|<5\) can be written as \(-5<x<5\).
Q 19
The inequality \(|x|>2\) represents two disjoint intervals on the number line.
Q 20
If \(a<b\) and \(c<0\), then \(ac>bc\).
Q 21
The system \(x\ge 2\) and \(x\le 5\) represents a closed interval \([2,5]\).
Q 22
The inequality \(x(x-1)>0\) is satisfied for \(0<x<1\).
Q 23
The inequality \(2x+3<2x-1\) has no solution.
Q 24
If \(f(x)=ax+b\) with \(a>0\), then \(f(x)>0\) represents a half-line on the number line.
Q 25
The inequality \(\frac{1}{x-1}>0\) has the solution \(x>1\).
Key Takeaways — LINEAR INEQUALITIES
Core facts for CBSE Boards & JEE
1
Multiplying/dividing both sides by a NEGATIVE reverses the inequality sign.
2
Adding or subtracting the same number does NOT change the inequality.
3
|x| < a means −a < x < a (open interval); |x| > a means x < −a or x > a.
4
Linear inequalities in two variables are represented by half-planes.
5
Solution of a system = intersection of the individual solution sets.
6
−x < 5 means x > −5 (multiply by −1, reverse sign).