Chapter 4 · ICSE Class 10 Mathematics (Selina Concise)

Linear Inequations

Solve linear inequations in one variable and represent solutions on the number line, working with the set of integers or real numbers.

📏 Chapter 4

A number line showing the solution to x greater than 3 A number line with an open circle at 3 and a shaded ray extending to the right, showing all values of x greater than 3 1 2 3 4 5
4.1

Solving Linear Inequations

Linear inequations are solved like equations, except that multiplying or dividing by a negative number reverses the inequality sign.

1

Solve: 2x−5 < 7

2x<12, x<6

2

Solve: −3x+6 ≥ 0

−3x≥−6, x≤2 (sign flips when dividing by −3)

4.2

Solution Sets on the Number Line

Solutions to inequations can be restricted to a specific set (like integers, natural numbers, or real numbers) and shown on the number line.

1

Solve 3x−2 ≤ 10, x ∈ N (natural numbers). List the solutions.

3x≤12, x≤4; since x∈N, solutions are {1,2,3,4}

2

Solve −2 < x ≤ 5, x ∈ Z (integers). List the solutions.

Integers strictly greater than −2 and up to 5: {−1,0,1,2,3,4,5}

Practice

Exercises

1. Solve: 4x+3 > 15

2. Solve: −2x+8 ≤ 0

3. Solve 2x−1 ≤ 9, x ∈ N. List solutions.

4. Solve −5 ≤ x < 3, x ∈ Z. List solutions.

5. Solve: 5−3x ≥ −4

Next chapter — Quadratic Equations 🔢 →