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

Equations and Solutions

What is an Equation?

An equation is a statement that two things are equal, shown with an equals sign (\( = \)). Equations often contain variables and ask you to find what value makes the equation true.

Solving Equations

The goal is to find the value of the variable that makes both sides of the equation equal. This value is called the solution.

Steps to Solve

  1. Simplify both sides if needed
  2. Use inverse operations to isolate the variable
  3. Check your solution by plugging it back in

Why Solve Equations?

Equations help us solve real problems, like figuring out how many items you can buy with a certain amount of money, or what number will balance a scale.

Word Problems

Equations can be made from real-life situations, making algebra a superpower for solving everyday puzzles!

Examples

  • Solve \( x + 5 = 12 \): Subtract 5 from both sides, \( x = 7 \).

  • If \( 3y = 15 \), then \( y = 5 \) because \( 3 \times 5 = 15 \).

In a Nutshell

Equations state that two expressions are equal, and solving them means finding the value for the variable.

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Inequalities