Math Antics: Understanding Inequalities

Introduction

• Inequalities are mathematical comparisons that determine relationships between numbers.
• The number line visually represents these relationships by showing how numbers increase from left to right.

Equations vs. Inequalities

• Equations:
  • Use the equal sign (=) to indicate equality between expressions.
  • Example: (1 + 1 = 2).
• Inequalities:
  • Use "greater than" (>) and "less than" (<) symbols.
  • Symbols indicate which number is larger or smaller.
  • Teacher’s tip: Imagine the symbols as alligator mouths wanting to eat the bigger number.

Explaining Inequalities

• Unlike equations, inequalities can't reverse the numbers without changing the symbol.
  • Example: (5 > 3) is true, but (3 > 5) is not.
• Combined Symbols:
  • "Greater than or equal to" ((\geq))
  • "Less than or equal to" ((\leq))

Graphing Inequalities

• Graphing illustrates inequalities on a number line.
• Inequality (n = 3): Graph as a single point at 3.
• Inequality (n > 3): Graph all numbers to the right of 3 as a line starting after 3, indicated with an open dot at 3.
• Multiple valid answers exist for inequalities, shown as continuous lines on graphs.

Compound Inequalities

• Compound Inequalities: Combine two inequalities to show a range of values.
  • Example: (3 < n < 7) signifies all numbers between 3 and 7, excluding 3 and 7 themselves.
  • Graph as a line between 3 and 7 with open dots at both ends.

Practical Uses

• Inequalities help with specifying conditions or number ranges:
  • Price range: Example for a bike: (50 < P < 200).
  • Temperature range: For a preferred home temperature: (68 < T < 72).

Conclusion

• Inequalities are versatile tools in math and practical situations.
• Regular practice will deepen understanding and skill in interpreting inequalities.

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