2.3

Inequalities

Cambridge IGCSE Mathematics (0580)  · Unit 2: Algebra and graphs  · 9 flashcards

Inequalities is topic 2.3 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 2 — Algebra and graphs , alongside Algebraic notation and manipulation, Equations and Sequences.  In one line: The symbol '≥' means greater than or equal to, and '≤' means less than or equal to. These symbols indicate that the solution *can* include the boundary value, unlike '>' and '<'.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 9 flashcards — 2 definitions, 2 key concepts and 2 application cards — covering the precise wording mark schemes reward.  Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

The symbols for 'greater than or equal to' and 'less than or equal to', and what does each mean

The symbol '≥' means greater than or equal to, and '≤' means less than or equal to. These symbols indicate that the solution *can* include the boundary value, unlike '>' and '<'.

Example: x ≥ 5 means x can be 5 or any number larger than 5.

Questions this Inequalities deck will help you answer

Definition Flip

What are the symbols for 'greater than or equal to' and 'less than or equal to', and what does each mean?

Answer Flip

The symbol '≥' means greater than or equal to, and '≤' means less than or equal to. These symbols indicate that the solution *can* include the boundary value, unlike '>' and '<'.

Example: x ≥ 5 means x can be 5 or any number larger than 5.
Key Concept Flip

Solve the inequality: 3x - 2 > 7

Answer Flip

To solve, isolate x. Add 2 to both sides: 3x > 9. Divide both sides by 3: x > 3. This means any value of x greater than 3 satisfies the inequality.

Key Concept Flip

Represent the inequality x ≤ -2 on a number line.

Answer Flip

Draw a number line. Place a closed circle (or filled dot) on -2 to show that -2 is included. Shade the line to the left of -2 to indicate all values less than -2.

Key Concept Flip

What are the integer solutions for the inequality -3 < x ≤ 2?

Answer Flip

Integer solutions are whole numbers. The integers that satisfy this inequality are -2, -1, 0, 1, and 2. Note that -3 is not included due to the '<' symbol.

Key Concept Flip

Explain how the rules change when multiplying or dividing both sides of an inequality by a negative number.

Answer Flip

When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign.

Example: if -2x < 6, then x > -3.
Key Concept Flip

Solve the inequality: 5 - 2x ≥ 11

Answer Flip

Subtract 5 from both sides: -2x ≥ 6. Divide both sides by -2 and reverse the inequality sign: x ≤ -3.

Key Concept Flip

The region R is defined by y > x + 1. Explain how to represent this inequality graphically.

Answer Flip

Draw the line y = x + 1. Use a dashed line to show it's *not* included due to the '>' sign. Shade the region *above* the line, as y is greater than x + 1.

Definition Flip

What is the meaning of the term 'boundary' in the context of inequalities and graphical representation?

Answer Flip

The boundary is the line that separates the region satisfying the inequality from the region that doesn't. It's represented by an equation (

Example: y = x + 1), and can be solid (included) or dashed (excluded) depending on the inequality sign.
Key Concept Flip

Describe the difference in graphical representation between x > 3 and x ≥ 3.

Answer Flip

x > 3 is represented by a dashed vertical line at x = 3, with shading to the right. x ≥ 3 is represented by a solid vertical line at x = 3, with shading to the right.

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2.2 Equations 2.4 Sequences

Key Questions: Inequalities

What are the symbols for 'greater than or equal to' and 'less than or equal to', and what does each mean?

The symbol '≥' means greater than or equal to, and '≤' means less than or equal to. These symbols indicate that the solution *can* include the boundary value, unlike '>' and '<'.

Example: x ≥ 5 means x can be 5 or any number larger than 5.
What is the meaning of the term 'boundary' in the context of inequalities and graphical representation?

The boundary is the line that separates the region satisfying the inequality from the region that doesn't. It's represented by an equation (

Example: y = x + 1), and can be solid (included) or dashed (excluded) depending on the inequality sign.

Tips to avoid common mistakes in Inequalities

More topics in Unit 2 — Algebra and graphs

Inequalities sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

2.1 Algebraic notation and manipulation

9 flashcards
2.2 Equations

9 flashcards
2.4 Sequences

18 flashcards
2.5 Quadratics

9 flashcards
2.6 Graphs of functions

9 flashcards
2.7 Straight line graphs

9 flashcards
2.8 Functions

9 flashcards
2.9 Differentiation

9 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

inequality greater than less than solve inequality number line integer solutions region shade boundary

Key terms covered in this Inequalities deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

The symbols for 'greater than or equal to' and 'less than or equal to', and what does each mean
The meaning of the term 'boundary' in the context of inequalities and graphical representation

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How to study this Inequalities deck

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