2.3

Inequalities

9 flashcards to master Inequalities

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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.

About Inequalities (2.3)

These 9 flashcards cover everything you need to know about Inequalities for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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