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Absolute Value Calculator

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An online absolute value calculator provides the absolute values of real values and functions separately for the given values. This absolute value inequalities calculator provides all the important information about inequalities and absolute functions. Here you can learn more about how to find absolute value inequalities and much more.

What are the Absolute Values?

In mathematics, the absolute value or modulus | x | of the real number x is the non-negative value of x, regardless of its sign. That is | x | = x means positive x, | x | = -x means negative x (in this case -x is positive), and | 0 | =0. In other words, the absolute value equation is defined as an equation containing an absolute value expression. For example, |x + 8| = 12. Here | x + 8 | is an absolute expression. The absolute value calculator only indicates the difference between the specified number and zero because negative values ​​are not allowed here.

Graph for Absolute Values:

The general form of absolute value notation equation is:

F(x) = k + a |x – h|

This equation used by the absolute value graph calculator, where, k and h tell about how the graph shifts vertically and horizontally. The variable “a” tells us how far the value graph stretches vertically, and whether the graph opens down or up.

Absolute Values Calculator

However, an online Mean Absolute Deviation Calculator helps you to find the absolute deviation of the given number around the mean, median, or any other number.

Absolute Value Equations and Absolute Value Inequalities:

Usually, this value is found by solving the absolute value equation as well as equations with these values ​​are called absolute equations; if instead of the equal (=)sign, we have less than (<), less than or equal to (≤), greater (<), or greater than or equal to (≥) sign, then it would be called an absolute value inequality.

In both cases, the absolute value inequalities calculator works similarly: when solving the equation, it simplifies the equation or numbers as much as possible. When we have to deal with these values, we isolate it on the side of the sign and divide it into possible options: positive and negative. This process is the same for absolute value inequalities and absolute value equations.

How to Solve Absolute Value Equations?

Solving absolute value equations is simple as using ordinary linear equations. The only additional important step is to divide the original absolute value equation into two parts: positive and negative (±) components.

  • Symbol ∣x∣ must be positive. For example, |x∣→+ ∣x∣.
  • x in the absolute value symbol | | can be any equation.
  • To be solved, the right side of the equation must be a positive number or zero.
  • If the “a” on the right is negative, then it has no results.

Example:

Solve the absolute value equation − x = −9.

Solution:

Don’t come to the conclusion that this equation has no solution too quickly. Although the right side of the equation is a negative number, the absolute value expression itself must be a positive number. this is not RIGHT?

  • The | x | sign must be positive. Emphasize | x ∣ → + ∣ x∣.
  • An absolute value calculator removes the minus sign from the absolute value sign before we can continue.
  • The coefficient of this equation is -1. So, the absolute value equation calculator divides both sides of the equation by this value to remove the negative sign.

-|x| = -9

-1 . |x| = -9

-1 . |x| / -1 = -9/-1

|x| = 9

  • Since the absolute value expression and the number are positive, the absolute value equations calculator uses a process to divide them into two equations.

|x| = a => x = +a, x = -a

  • So, the solution of the problem becomes

|x| = 9 => x = 9, x = -9

However, an Online Hyperbola Calculator will help you to determine the center, eccentricity, focal parameter, major, and asymptote for given values in the hyperbola equation.

How to Solve Absolute Value Inequalities?

Solving absolute value inequalities step-by-step with follow up the given steps:

  • First, on the left side of the inequality, isolate the absolute value expression.
  • If the number is on the other side of the inequality sign is negative, then the equation has no solution. Use the sign of every side of your inequality to decide which of these cases holds. If the number is positive on the other side of the inequality, then we jump to the next step.
  • Remove the absolute values by setting up a compound inequality. The type of inequality sign in the problem describes how to set up the inequality.

If the given problem has a greater than sign, then set up an or compound inequality as:

(absolute value) < (number on other side)

Or

(Absolute value) > (number on other side)

Use the same steps for ≥ sign.

If your absolute value is less than a number, then set up a three-part compound inequality that looks like this:

(other side number) < (inside absolute value quantity) < (number on other side)

The same setup is used for a ≤ sign

  • Solve the inequalities with an absolute value inequality calculator.

How Absolute Value Calculator Works?

An online absolute value equation calculator changes the input values into the positive number and check the particular points of the absolute value graph and equation with the following steps:

Input:

  • Click the “number tab”, if you want to perform a mathematical operation on a given number, or select “for equation” tab, when you want to solve an equation.
  • Now, substitute the given values in the selected tab fields.
  • Click on the calculate button for the solution.

Output:

  • The absolute value calculator solves the number or equation for absolute values according to your selection.

FAQ:

What is the rule of absolute value?

The absolute value of a number is the distance from zero on the number line.

Why is the absolute value never negative?

The absolute value represents the distance but does not contain direction information. Because the direction is ignored, the absolute value of any number can only be positive or zero, not negative.

Conclusion:

Use this online absolute value calculator to solving your equations or number, and develop a better understanding of the whole concept. In algebra, it is not an easy task to deal with absolute values. Many mathematicians believe that the concept of absolute values is not difficult, but it requires deep understanding and more interest.

Reference: 

From the source of Wikipedia: Terminology and notation, Definition and properties, Complex numbers, Proof of the complex triangle inequality, Absolute value function.
From the source of HMH: What Does Absolute Value Mean, Absolute Value Examples and Equations, Materials, Standards, Prerequisite Skills, and Concepts.

From the source of Purple Math: Relationship to the sign function, Derivative, Antiderivative, Distance, Ordered rings, Fields, Vector spaces.