Linear Inequalities — Class 11 Mathematics
Core Concepts
Unlike an equation, an inequality describes a range of values. Multiplying or dividing an inequality by a negative number reverses its sign.
Worked Examples
3x−5<10 ⇒ 3x<15 ⇒ x<5.
−2x+4≥8 ⇒ −2x≥4 ⇒ x≤−2. The sign reverses because we divided by −2.
Two Variables
An inequality such as x+y≤4 represents a half-plane. The boundary x+y=4 is included because of ≤; a strict inequality excludes its boundary.
Explained MCQs
- When dividing by a negative number, the inequality sign must reverse.
- The solution of x≥3 is represented by a closed point at 3 and shading to the right.
- For x+y<5, the boundary line is not included.
Practice
- Solve 5−2x>11.
- Graph 2x+y≤6 and identify the feasible side.