Master

Solving Equations

Master solving equations with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Solving Equations

Study Guide

Key Definition

An equation is a mathematical statement formed by placing an equal sign between two numerical or variable expressions, such as $3x + 5 = 11$.

Important Notes

An equation can have one solution, multiple solutions, or no solutions.
The solution to $3x + 5 = 11$ is $x = 2$.
The equation $x^2 = x$ has solutions $x = 0$ and $x = 1$.
The equation $x + 1 = 1 + x$ is true for all real numbers.
The equation $x + 1 = x$ has no solution.

Mathematical Notation

$=$ represents equality

$+$ represents addition

$\times$ or $*$ represents multiplication

$\frac{a}{b}$ represents fractions

$x^2$ represents exponents

Remember to use proper notation when solving problems

Why It Works

Solving equations involves finding the value of a variable that makes the equation true, using operations like addition or subtraction to isolate the variable on one side.

Remember

The solution set of an equation includes all values that satisfy the equation.

Quick Reference

Single Solution Example:$3x + 5 = 11$: $x = 2$

Multiple Solutions Example:$x^2 = x$: $x = 0$, $x = 1$

Understanding Solving Equations

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation: To solve the linear equation $3x + 5 = 11$, subtract 5 from both sides to get $3x = 6$, then divide by 3 to find $x = 2$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve for $x$: $3x + 5 = 11$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You currently have $3x + 5$ dollars and you need a total of $11$ dollars. If $x$ represents the number of additional dollars you need, how many dollars is $x$?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the equation $x^2 = x$. What are the solutions?

Challenge Quiz

Single Choice Quiz

Advanced

Which equation has no real solution? $x + 1 = x + 2$ or $x + 1 = x$

Recap

Watch & Learn

Review key concepts and takeaways