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Inequalities - Introduction

Inequalities are mathematical statements, which can be either true or false.
They are used to compare two quantities \(x\) and \(a\) to state either of the following:

  • \(x\) is greater than \(a\).
  • \(x\) is less than \(a\).
  • \(x\) is greater than or equal to \(a\).
  • \(x\) is less than or equal to \(a\).

Inequalities - Symbols

When working with inequalities, four symbols must be known:

  • \(x > a \) : \(x\) is greater than \(a\).
  • \(x < a \) : \(x\) is less than \(a\).
  • \(x \geq a \) : \(x\) is greater than or equal to \(a\).
  • \(x \leq a \) : \(x\) is less than or equal to \(a\).

Example

State whether each of the following statements is true or false.

  1. \(2 > 5\)
  2. \(7>3\)
  3. \(3< 4\)
  4. \(6<5 \)
  5. \(5 \geq 4\)
  6. \(8 \geq 10\)
  7. \(2 \geq 2 \)
  8. \(6 \leq 5 \)
  9. \(5 \leq 6 \)
  10. \(12 \leq 12 \)

Solution +

Solution

Example

Complete either of the following with either of the four symbols \(>\), \(< \), \(\geq \) or \(\leq \) to make each statement true.
Note: each of these has two possible solutions.

  1. \(2 \quad ... \quad 7 \)
  2. \(10 \quad ... \quad 8 \)
  3. \(5 \quad ... \quad 6 \)
  4. \(9 \quad ... \quad 9 \)
  5. \(-3 \quad ... \quad 2 \)
  6. \(15 \quad ... \quad 13 \)
  7. \(-20 \quad ... \quad 1 \)
  8. \(0 \quad ... \quad -5 \)
  9. \(-10 \quad ... \quad -8 \)

Solution +

Solution