Inequalities - Introduction

(What's an Inequality?)


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

  • \(A\) is greater than \(B\).
  • \(A\) is less than \(B\).
  • \(A\) is greater than or equal to \(B\).
  • \(A\) is less than or equal to \(B\).

Inequalities - Symbols

When working with inequalities, four symbols must be known:

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

Exercise 1

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. \(12 \leq 12 \)

Answers Without Working

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


Exercise 2

Complete either of the following with nothing but one of the four symbols \(>\), \(< \), \(\geq \) or \(\leq \) to make each statement true.
Note: each of these has two possible solutions, write each of the 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. \(-10 \quad ... \quad -8 \)

Answers Without Working

  1. \(2 < 7 \) and \(2 \leq 7 \)
  2. \(10 > 8 \) and \(10 \geq 8 \)
  3. \(5 < 6 \) and \(5 \leq 6 \)
  4. \(9 \leq 9 \) and \(9 \geq 9 \)
  5. \(-3 < 2 \) and \(-3 \leq 2 \)
  6. \(15 > 13 \) and \(15 \geq 13 \)
  7. \(-20 < 1 \) and \(-20 \leq 1 \)
  8. \(0 > -5 \) and \(0 \geq -5 \)
  9. \(-10 < -8 \) and \(-10 \leq -8 \)


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