Class 11 Maths | NCERT Exercise 5.1 | Linear Inequalities Full Solutions

In this lecture, we solve every question of Chapter 5, Ex 5.1 (Linear Inequalities) with clear reasoning, number-line graphs, and domain-wise answers for N (naturals), Z (integers), and R (reals).

What you’ll learn

Core ideas: definition, symbols , and when/why inequality reverses on multiplying/dividing by a negative.
Methods: isolate the variable; write solution sets in N/Z (enumeration) and in R (interval notation).
Graphs: open vs closed circles on the number line; brief context of solid/dotted boundaries.

Timestamps (chapters)

00:00 Ex 5.1 Q1 | Solve 24x less than 100
04:41 Ex 5.1 Q2 | Solve – 12x greater than 30
07:27 Ex 5.1 Q3 | Solve 5x – 3 less than 7,
10:01 Ex 5.1 Q4 | Solve 3x + 8 greater than 2
12:22 Ex 5.1 Q5 | 4x + 3 less than 5x + 7
13:46 Ex 5.1 Q6 | 3x – 7 greater than 5x – 1
15:02 Ex 5.1 Q7 | 3(x – 1) ≤ 2 (x – 3)
16:04 Ex 5.1 Q8 | 3 (2 – x) ≥ 2 (1 – x)
17:19 Ex 5.1 Q9 | x + (x/2) + (x/3) less than 11
18:36 Ex 5.1 Q10 | (x/3) greater than (x/2) + 1
19:51 Ex 5.1 Q11 | (3/5)(x-2) ≤ (5/3)(2-x)
22:14 Ex 5.1 Q12 | (1/2)((3/5)x + 4) ≥ (1/3)(x-6)
24:03 Ex 5.1 Q13 | 2 (2x + 3) – 10 less than 6 (x – 2)
25:52 Ex 5.1 Q14 | 37 – (3x + 5) greater than 9x – 8 (x – 3)
28:25 Ex 5.1 Q15 | (x/4) less than (5x-2)/3 - (7x-3)/5
31:20 Ex 5.1 Q16 | (2x-1)/3 ≥ (3x-2)/4 - (2-x)/5
34:27 Ex 5.1 Q17 | 3x – 2 less than 2x + 1
36:09 Ex 5.1 Q18 | 5x – 3 ≥ 3x – 5
38:06 Ex 5.1 Q19 | 3 (1 – x) less than 2 (x + 4)
40:09 Ex 5.1 Q20 | (x/2) ≥ (5x-2)/3 - (7x-3)/5
43:33 Ex 5.1 Q21 | Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.
46:44 Ex 5.1 Q22 | To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks).
51:56 Ex 5.1 Q23 | Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11
57:42 Ex 5.1 Q24 | Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23
01:03:24 Ex 5.1 Q25 | The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side
01:07:08 Ex 5.1 Q26 | A man wants to cut three lengths from a single piece of board of length 91cm

How solutions are shown

Rule checks at each step (when direction changes, why).
Set-specific answers: list all values for N/Z; use intervals for R.
Graphs: correct open/closed endpoints for strict/inclusive cases.

Learning outcomes

Solve any one-variable linear inequality across N, Z, R.
Write solution sets correctly and graph them.
Avoid sign-flip and fraction mistakes—most common exam errors.
Build a base for two-variable inequalities and later Linear Programming.

For whom

CBSE Class 11, NCERT seekers, and early practice for JEE/NDA fundamentals.
📂 Playlist (Chapter 5 – Linear Inequalities): [add link]
📝 Class notes / PDF (Eng/Hindi): [add link]
🧩 Worksheet & answers: [add link]

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