# Understand the Absolute Value Formulas & Rules to Solve the Absolute Value Equations

## Introduction

In this article, you will learn what absolute value inequality is and how to solve absolute value inequalities. Also understand the absolute value equation rules.

## Absolute Value Definition

An algebraic expression, containing inequality symbols, is called an absolute value inequality. It is a simple linear equation that follows the rules of absolute numbers. There are four types of inequality symbols in this expression of absolute value definition. These are >,<,≤, ≥.

## Absolute Value Formulas

This formula contains an absolute value equation. It is a way of writing an inequality in algebraic expression. The absolute value equation formula is generally expressed as: ## Absolute Value Equation Rules

To solve the absolute value inequality equations, remember the following rules to express the solution of a given equation. These are:

1. When the inequality is in the form of |x| < a or |x| < a
2. In this case,

If

|x| < a -a < x < a

And if

|x| < a -a < x < a

3. When the inequality is in the form of |x| > a or |x| > a
4. If

|x|> a x < -a or x > a

And if

|x| > a x < -a or x > a.

5. When the inequality is in the form of |x| < - a or |x| < - a
6. Since the absolute value always results in a positive value. But when the value of x is less than or equal to -a. It means that there will be no solution for x.

7. When the inequality is in the form of |x| > - a or |x| > - a
8. Here, in this case, the value of x is greater than or equal to –a, so the solution of x will be all real numbers.

## How to Solve an Equation with Absolute Value?

The absolute value equation rules are essential to solving these inequalities. Here we provide a step-by-step way of solving absolute value inequalities.

• First, remember that the inequality has to be solved for the values of the variables involved.
• Isolate the absolute value on one side and the remaining values on the right side.
• Write the equation in compound inequality by using inequality signs.
• Find the values of the variable x and graph the solution on a real line.
• Here are some examples to understand how to solve the absolute value equation.

## Example of Absolute Value Equation ## Formulas Related to Absolute Value Equation Formula

1. Absolute value
2. The absolute value formula for a number c is,

c = c c ≥ 0 -c c< 0

3. Double absolute value inequalities
4. The double absolute value inequalities can be expressed in general form as,

ax + b + c < d

It can be expressed using all four inequality symbols like >,<,≤, ≥.

## What is the absolute value of -3?

By the definition of absolute value,

|-3|=3

Because the number 3 is greater than zero. It does not matter the negative sign because the absolute value formula always gives a positive number.

## What is the absolute value equation?

It is an algebraic expression with inequality symbols. The general form of absolute value inequality is:

ax + b < c

Or,

ax + b > c

Or,

ax + b ≤ c

Or,

ax + b ≥ c

## What is the Absolute Value of -5?

The absolute value of -5 is 5. It is because by the definition of absolute value,

|-5|=5 ### Alan Walker

Last updated: July 07, 2023

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