 # Absolute Value Equations

A series of free Basic Algebra Lessons with examples and solutions.

In these lessons, we will learn

• Definition of absolute value.
• Solving absolute value equations
• Solving absolute value equations with two absolute value expressions
• Applications of absolute value equations

We also have an absolute value equation calculator that can solve and graph absolute value equations. Use it to check your answers.

## Definitions and Applications of Absolute Value

Sometimes we need to use only positive numbers, and the absolute value is a useful tool for this purpose. When you see an absolute value in a problem or equation, it means that whatever is inside the absolute value is always positive. Absolute values are often used in problems involving distance and are sometimes used with inequalities. In another lesson, we will discuss graphs of absolute value equations and inequalities.
This video introduces the idea of absolute value including a couple of definitions.

## Absolute Value Equations

Solving for a variable in absolute value equations follows different rules than when we solve multi-step equations. When solving absolute value equations, most of the time we get more than one possible solution. Using absolute value equations, we are able to solve more complex concepts such as absolute values with inequalities, and graphs of absolute value inequalities with two variables.

Example of solving an absolute value equation (part 1)
Example of solving an absolute value equation (part 2)

Solving Absolute Value Equations - Example 1
Solving Absolute Value Equations - Example 2

## Absolute Value Equations with Two Absolute Value Expressions

Solving Absolute Value Equations Containing TWO Absolute Value Expressions - Example 1

Solving Absolute Value Equations Containing TWO Absolute Value Expressions - Example 2

Solving Absolute Value Equations Containing TWO Absolute Value Expressions - Example 3

## Applications of Absolute Value Equations

Foust Honda is having a contest to win a new Honda Civic. To win a chance at the car, you must guess the nunber of keys in the jar within 5 of the actual number. The people who are within this range get to try a key ih the ignition of the Civic. Suppose there are 697 keys in the jar.
a) Write an equation to determine the highest and lowest guesses that will will a chance at the car.
b) Solve the equation

Absolute Value Word Problem
The average January temperature in a northern Canadian city is 1 degree fahrenheit. The actual January temperature for that city may be 5 degrees warmer or colder. Write and solve an equation to find the minimum and maximum temperatures.

## Absolute Value Equation Calculator

This absolute equation calculator will help you solve and graph absolute value equations.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 