Algebra

Fundamental algebraic concepts including equations, inequalities, and functions.

Variables and ExpressionsEquations and SolutionsInequalities
Functions and GraphsSystems of EquationsQuadratic Equations
Budgeting and Saving MoneyTravel Planning with EquationsCooking and Recipes
Checking Your WorkBreaking Problems Into Steps
Variables and Expres...Equations and Soluti...InequalitiesFunctions and GraphsSystems of EquationsQuadratic EquationsBudgeting and Saving...Travel Planning with...Cooking and RecipesChecking Your WorkBreaking Problems In...
Basic Concepts

Inequalities

What are Inequalities?

An inequality shows that two values are not necessarily equal. Instead, one is greater, less than, or possibly equal to the other.

  • \( x > 5 \) means \( x \) is greater than 5.
  • \( y \leq 8 \) means \( y \) is less than or equal to 8.

Solving Inequalities

Similar to equations, but you use \( >, <, \geq, \leq \) instead of \( = \). When you multiply or divide both sides by a negative number, remember to flip the inequality sign!

Graphing Solutions

Solutions to inequalities are often shown on number lines, which helps you see all possible answers at once.

Why Use Inequalities?

Inequalities help answer questions like "How many tickets can I buy with \$10?" or "What temperatures are safe for ice cream?"

Real-World Connection

When you see a sign that says "You must be at least 12 years old to ride," that's an inequality: \( x \geq 12 \).

Examples

  • Solve \( x - 3 < 7 \): Add 3 to both sides, \( x < 10 \).

  • If \( 2y \geq 8 \), then \( y \geq 4 \) because \( 2 \times 4 = 8 \).

In a Nutshell

Inequalities compare values and show when one side is bigger or smaller than the other.

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Functions and Graphs