# How to write an absolute value equation

Equations with Absolute Value: Lesson 2 of 2 Solving equations with absolute value is a more advanced skill. Absolute value equations Video transcript Let's do some equations that deal with absolute values. And just as a bit of a review, when you take the absolute value of a number. Let's say I take the absolute value of negative 1. What you're really doing is you're saying, how far is that number from 0?

And in the case of negative 1, if we draw a number line right there-- that's a very badly drawn number line. If we draw a number line right there, that's 0. You have a negative 1 right there. Well, it's 1 away from 0. So the absolute value of negative 1 is 1.

And the absolute value of 1 is also 1 away from 0. It's also equal to 1. So on some level, absolute value is the distance from 0. But another, I guess simpler way to think of it, it always results in the positive version of the number.

The absolute value of negative 7, is equal to 7, So with that in mind, let's try to solve some equations with absolute values in them. So let's say I have the equation the absolute value of x minus 5 is equal to And one way you can interpret this, and I want you to think about this, this is actually saying that the distance between x and 5 is equal to So how many numbers that are exactly 10 away from 5?

And you can already think of the solution to this equation, but I'll show you how to solve it systematically. Now this is going to be true in two situations.

Either x minus 5 is equal to positive If this evaluates out to positive 10, then when you take the absolute value of it, you're going to get positive Or x minus 5 might evaluate to negative If x minus 5 evaluated to negative 10, when you take the absolute value of it, you would get 10 again.

So x minus 5 could also be equal to negative Both of these would satisfy this equation. Now, to solve this one, add 5 to both sides of this equation. You get x is equal to To solve this one, add 5 to both sides of this equation.

So our solution, there's two x's that satisfy this equation. Negative 5 minus 5 is negative Take the absolute value, you get And notice, both of these numbers are exactly 10 away from the number 5.

## Absolute Value Equations

Let's do another one of these. Let's do another one.How to solve an absolute value equation. How to solve an absolute value inequality.

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S k i l l i n A L G E B R A. Table of Contents | Home. ABSOLUTE VALUE. The geometrical meaning. And so if we write |x − 2| = 4. we mean that x is 4 units aways from 2. x therefore is equal either to −2 or 6. On the other hand, if we write. Algebra > Absolute Value Equations and Inequalities > Solving Absolute Value Equations > Absolute Value Equations.

Absolute Value Equations. This Algebra Cruncher generates an endless number of practice problems for absolute values equations -- with solutions and hints! Advertisement.

Write and solve an absolute-value equation to find the minimum and maximum heights of the bridge. Your Turn: Case 1 x – = + =+ x = Since is subtracted from x add to both sides of each equation.

The minimum height of the bridge is meters. Learn how to avoid those mistakes here by working on examples of absolute value equations with operations on the inside and the outside of the absolute value.

7. How to Graph an Absolute Value and. Graphing absolute value functions or equations, examples Quadratic equations with absolute value Graphical interpretation of the definition of the absolute value of a function y = f (x) will help us solve an equation with absolute value.

Want to write an equation to translate the graph of an absolute value equation? This tutorial takes you through that process step-by-step! Take an absolute value equation and perform a vertical and horizontal translation to create a new equation.

Watch it all in this tutorial.

Algebra Trig Review