Inequalities (Copy)

Inequalities Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Representing and Interpreting Inequalities (Including Number Lines)

1. Understanding Inequality Symbols

2. Representing Inequalities on a Number Line

• Open Circle (⭘) = Strict inequality (<, >)
• Closed Circle (●) = Inclusive inequality (⩽, ⩾)
• Always draw a line or arrow from the point to show the range of values.

3. Examples

Example 1:

x < 2

• Draw a number line
• Open circle at 2
• Arrow going left

Example 2:

x ⩾ –3

• Draw a number line
• Closed circle at –3
• Arrow going right

Example 3 (Double Inequality):

–3 ⩽ x < 1

• Closed circle at –3
• Open circle at 1
• Line connecting both points

4. Writing Inequalities from a Number Line

• Closed circle at 4, arrow to the left → x ⩽ 4
• Open circle at –2, arrow to the right → x > –2
• Closed circle at –1, open circle at 3, line between → –1 ⩽ x < 3

5. Solving Simple Inequalities

Treat like equations but flip the inequality sign if multiplying or dividing by a negative number.

• Example 1:
  2x + 3 < 7
  → 2x < 4
  → x < 2
• Example 2 (Negative coefficient):
  –3x > 9
  → x < –3 (flipped sign because divided by negative)

6. Quick Tips

• Always check the sign to know which direction to shade or draw arrows.
• Use inequality signs, not equals, unless told otherwise.
• Inequalities represent ranges, not fixed values.
• When graphing, make sure circles and arrows are clear.

Core-level Questions Will Ask You To:

• Solve and graph simple inequalities.
• Interpret number lines.
• Translate between words, algebra, and graphs.
• Avoid complex rearrangements or systems (these are for extended).