Algebra 1

Algebra 1 introduces students to the fundamental concepts of algebra, including variables, equations, and functions.

Understanding VariablesSolving EquationsFunctions and Their Graphs
Systems of EquationsInequalities and Their GraphsQuadratic Equations
Using Algebra in ShoppingAlgebra in Sports and GamesMaking Predictions with Patterns
Step-by-Step Problem SolvingChecking Your Work
Understanding Variab...Solving EquationsFunctions and Their ...Systems of EquationsInequalities and The...Quadratic EquationsUsing Algebra in Sho...Algebra in Sports an...Making Predictions w...Step-by-Step Problem...Checking Your Work
Advanced Topics

Inequalities and Their Graphs

What Are Inequalities?

Inequalities are like equations, but instead of an equals sign, they use symbols like \( < \), \( > \), \( \leq \), or \( \geq \). They show that one side is bigger, smaller, or possibly equal to the other.

How to Solve Inequalities

  • Use similar steps as with equations.
  • If you multiply or divide both sides by a negative number, flip the inequality sign!

Graphing Solutions

Solutions can be shown on a number line or a coordinate grid. Shaded areas show all the possible answers.

Real-Life Uses

Inequalities are used for things like budgeting (spending less than you earn) or setting limits (height requirements for rides).

Examples

  • Solve \( x + 3 < 8 \) to get \( x < 5 \).

  • Graph \( y \geq 2x \) as a shaded area above the line \( y = 2x \).

In a Nutshell

Inequalities express relationships where values can be greater or less than others.

Next
Quadratic Equations