## Introduction to Absolute Value Inequalities Calculator

Absolute value inequalities calculator is an online algebraic tool that is used to **find the absolute value** of a function present with inequalities or we can say for solving absolute value inequalities.

The absolute value inequality calculator determines the mathematical linear expression with one variable and gives the solution in the form of inequality in a few seconds.

## What is Absolute Value Inequalities?

Absolute value inequality is defined as the **inequalities with absolute value** of linear mathematical expression with variables. Absolute value inequalities are present in inequalities signs (>,< ) with the absolute value functions.

## Formula Used by Absolute Value Inequality Calculator

Absolute value inequality **consists of an inequality sign** along with the absolute values in a mathematical expression. Our absolute value inequalities calculator represents the result in a graph according to the three cases below:

### Case 1:x<a

If the value of x is less than a then the arrow goes toward the negative side in a number line

### Case 2: a≤x<b

If the value of a is less than x and the value of b value is greater then the arrow goes in between the negative and positive side of a number line.

### Case3:x≥b

If the value of x is greater than a then the arrow goes toward the positive side in a number line.

$$ |x| \;=\; \biggr[ \begin{matrix} x, & x \ge 0 \\ -x, & x \lt 0 \end{matrix} $$

## Working Behind the Absolute Inequality Calculator

The absolute value inequality solver uses the easiest method to solve the problem of the absolute value inequality equation so that you can easily understand the concept of the absolute value inequalities expression instantly.

When you add the input value of an absolute value inequality in our inequality absolute value calculator, it starts analyzing the given algebraic equation, for example, **4|x+3|-7<5**. After opening the inequality mode, the given equation is divided into two with positive and negative signs (-3x+35) respectively, after simplification of the given mathematical expression as |x+3|<3.

Then it solves the linear algebraic equation according to the rules of algebra and gives the solution in increasing and decreasing order as given in the below example x= 0 and x= -6.

Our tool uses these points to **draw an intersecting line on the number line** so that you get a visual understanding of the absolute value inequalities concept. Let's take an example of an absolute value inequalities problem to know the working procedure of the absolute value inequalities calculator.

## Example of Solving Absolute Value Inequalities:

An **example of an absolute value inequalities** problem is given to understand the step-by-step manual calculations of solving such problems. Although our absolute inequality calculator can solve absolute value inequalities but its crucial to understand the manual process.

### Example:

Solve the following:

$$ 4 |x+3| -7 \le 5 $$

**Solution:**

Isolate the absolute value,

$$ 4 |x+3| -7 \le 5 $$

$$ 4|x+3| \le 12 $$

$$ |x+3| \le 3 $$

Applying the theorem and rewriting the value,

$$ |x+3| \lt 3 $$

$$ -3 \le x+3 \le 3 $$

Solving the equation,

$$ -3 \le x+3 \le 3 $$

$$ -3 -3 \le x+3 -3 \le 3 - 3 $$

$$ -6 \le x \le 0 $$

The graphical representation of this is given,

## How to Use the Absolute Value Inequalities Calculator?

The absolute value inequality calculator has a simple layout so anyone can use it easily to solve different types of inequalities (<,>,≥, ≤). You need to follow some of our guidelines for using the calculator. These guidelines are given as

**Enter the absolute value of the inequality**function in the respective field- Select the select the inequality sign as per your function from the given list.
- Click to calculate button to get the solution of the absolute value inequalities problem
- Click on the recalculate button to get a new page for more absolute value inequalities problem calculations.
- Check you input function first before hitting the calculate button.

## Result from Absolute Value Inequality Solver:

The absolute value inequalities calculator provides you with the result of your given algebraic expression in a fraction of a second after you click on the calculated button. It may include the following:

- Result option provides you with a solution for the absolute value inequality problem
- Possible steps option provides you with solutions for algebraic absolute value inequality in a step-wise process.
- Number line option will draw a line on the number line table as per the given result so that you understand it clearly.

## Advantages of Inequality Absolute Value Calculator:

The absolute inequality calculator provides you with tons of advantages whenever you use it to calculate the algebraic expression of inequality. These benefits are given below.

- The absolute value inequality solver
**saves time and effort**that you consume while doing complex calculations of absolute value inequalities problems manually. - It can solve different types of inequalities in the absolute value of linear equations.
- Our absolute value inequality calculator can operate anywhere through a computer, laptop, or mobile with the internet for the solution of absolute value inequalities problems
- This absolute value inequalities calculator has a user-friendly interface so that you can solve it absolute value expression of inequality easily.