# Solving Problems With Absolute Value

If c is a positive number, then | x | = c is equivalent to x = c or x = – c. Break the equation up into two equivalent equations using the rule: If | x | = c then x = c or x = - c . If the absolute values of two expressions are equal, then either the two expressions are equal, or they are opposites.| x – 6 | = 4 is equivalent to x – 6 = 4 or x – 6 = – 4 Step 2. x – 6 6 = 4 6 x = 10 x – 6 6 = – 4 6 x = 2 Step 3 . | 10 – 6 | = | 4 | = 4 | 2 – 6 | = | – 4 | = 4 The solutions are x = 10 and x = 2 . Break the equation up into two equivalent equations using the rule: If | x | = c then x = c or x = - c . If x and y represent algebraic expressions, | x | = Step 1.Solving absolute value inequalities is a lot like solving absolute value equations, but there are a couple of extra details to keep in mind.

A very basic example would be as follows: if required.

However, these problems are often simplified with a more sophisticated approach like being able to eliminate some of the cases, or graphing the functions.

When solving equations that involve absolute values, there are two cases to consider.

Case 1: The expression inside the absolute value bars is positive.

To get each piece, you must figure out the domain of each piece.

This method is highly beneficial when the question writer asks for the number of solutions instead of the actual solutions.Thus, the solutions are Sometimes absolute value equations have a ridiculous number of cases and it would take too long to go through every single case.Therefore, we can instead graph the absolute value equations using the definition of absolute value as a piecewise function.The absolute value function exists among other contexts as well, including complex numbers.Note that and For complex numbers , the absolute value is defined as , where and are the real and imaginary parts of , respectively.Let's work through some examples to see how this is done. Another benefit of this graphing technique is that you do not need to verify any of the solutions--since we are only graphing the pieces that are actually mathematically possible, we get all the solutions we are looking for, no less and no more.If you could not discern the solutions from the picture, you can simply solve the equation for each case.If you are not a member or are having any other problems, please contact customer support.This equation is asking us to find all numbers, x , that are 3 units from zero on the number line.Because we are multiplying by a positive number, the inequalities will not change: −2 ≤ x ≤ 6 Done!Equations with a variable or variables within absolute value bars are known as absolute value equations .

## Comments Solving Problems With Absolute Value

• ###### Absolute Value Equations Brilliant Math & Science Wiki

Absolute value equations are equations involving expressions with the absolute value functions. This wiki intends to demonstrate and discuss problem solving.…

• ###### Absolute value - Art of Problem Solving

The absolute value function exists among other contexts as well, including. Problems. Find all real values of \$x\$ if \$-x = x-6\$. Find all real values of \$x\$.…

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Use an absolute value equation to find least and biggest amount of money in your pocket? Solution Let x be the possible amount of money in your pocket.…

• ###### Absolute Value Equation Calculator - MathPapa

Shows you the step-by-step solutions solving absolute value equations! This calculator will solve your problems.…

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Solving Absolute Value Equations 1 - Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons.…

• ###### How to Solve Absolute Value Inequalities - Sciencing

Solving absolute value inequalities is a lot like solving absolute value equations, but there are a couple of extra details to keep in mind. It helps.…

• ###### Absolute Value Equations

Follow these steps to solve an absolute value equality which contains one absolute value Isolate the absolute value on one side of the equation. Is the number.…

• ###### Solve an absolute value equation College Algebra

Knowing how to solve problems involving absolute value functions is useful. For example, we may need to identify numbers or points on a line that are at a.…