CBSE Math RevisionLinear Inequalities: CBSE Class 11 Maths knowledge organiser
Everything to know about linear inequalities on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.
Key definitions
- Linear inequality
- A statement such as ax + b < 0 using <, >, ≤ or ≥ instead of =.
- Solution set
- All the values of the variable that make the inequality true.
- Reversing the sign
- Multiplying or dividing both sides by a negative number reverses the inequality.
Key formulas
| × or ÷ by a negative number reverses the sign; system = intersection; ● included, ○ excluded |
Worked example
Solve \(5 - 2x \le 11\), \(x \in \mathbb R\).
\(-2x \le 6 \Rightarrow x \ge -3\): \([-3, \infty)\).
Common mistakes
- Not reversing the sign when dividing by a negative number.
- Wrong end-points in the answer: \(\lt\) gives an open circle and a round bracket.
- For a system, giving the union instead of the intersection.
- Giving a decimal number of people: round in the direction the inequality allows.
You should be able to…
- Solve one-step and two-step linear inequalities and write the solution as an interval.
- Clear fractions, solve double inequalities and systems, and show them on a number line.
- Model budgets, marks and speeds with inequalities and give whole-number answers where needed.
- Solve systems of three inequalities and count integer solutions.
The printable sheet
Revise it next
- Linear Inequalities: Class 11 notes
- Practise Linear Inequalities by step (Route to 95)
- Skill Builders
- CBSE Class 11 Maths formula sheet (PDF)
Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers