CBSE - Class 11 Mathematics Linear Inequalities Worksheet
1.
Solve the inequality $3 (1 – x) < 2 (x + 4)$ and show the graph of the solution on number line.
2.
Solve $– 12x > 30$, when (i) $x$ is a natural number.
3.
Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.
4.
Solve the inequality $\frac{x}{4} < \frac{(5x-2)}{3} - \frac{(7x-3)}{5}$ for real $x$.
5.
Solve the inequality $x + \frac{x}{2} + \frac{x}{3} < 11$ for real $x$.
6.
The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.
7.
Solve the inequality $3 (2 – x) \ge 2 (1 – x)$ for real $x$.
8.
Solve the inequality $\frac{3(x-2)}{5} \le \frac{5(2-x)}{3}$ for real $x$.
9.
Solve the inequality $2 (2x + 3) – 10 < 6 (x – 2)$ for real $x$.
10.
Solve the inequality $37 – (3x + 5) > 9x – 8 (x – 3)$ for real $x$.
11.
Solve the inequality $\frac{x}{3} > \frac{x}{2} + 1$ for real $x$.
12.
Solve the inequality $4x + 3 < 5x + 7$ for real $x$.
13.
Solve the inequality $3x – 7 > 5x – 1$ for real $x$.
14.
Solve $5x – 3 < 7$, when (i) $x$ is an integer.
15.
Solve $3x + 8 > 2$, when (ii) $x$ is a real number.
16.
Solve $– 12x > 30$, when (ii) $x$ is an integer.
17.
Solve the inequality $\frac{(2x-1)}{3} \ge \frac{(3x-2)}{4} - \frac{(2-x)}{5}$ for real $x$.
18.
Solve $3x + 8 > 2$, when (i) $x$ is an integer.
19.
Solve the inequality $3x – 2 < 2x + 1$ and show the graph of the solution on number line.
20.
Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
