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## Algebra (all content)

### Course: Algebra (all content)>Unit 8

Lesson 2: Solving absolute value equations

# Intro to absolute value equations and graphs

To solve absolute value equations, find x values that make the expression inside the absolute value positive or negative the constant. To graph absolute value functions, plot two lines for the positive and negative cases that meet at the expression's zero. The graph is v-shaped. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• How could I work on these functions with two or more absolute values?

like graphing f(x) = |2x-1| -3|x+1|
• You'll have to consider 4 cases. In one, 2x+1=0 and -(2x+1)=0 . Do that same for the other absolute value and thus you'll obtain 4 answers, i.e, the line will intersect the x axis at 4 points.
• I don't really understand this. Can anyone help me?
• If it's a negative number that you're trying to find the absolute value of, and there are no other terms attached to it, then the answer is the positive of that number. The same goes for positive numbers, except they stay positive. For example, the absolute value of -2 is 2, and the absolute value of 2 is also 2. I hope this helped!
• At , why is the Y intercept equal to 0? From that point on it makes perfect sense how he would then reach the conclusion that X=-3. I just don't understand why Y=0 in that equation. Mucho appreciation for any help!
• You can't say "y-intercept is equal to 0", it's not correct. That x=-3 you're talking about is the x-intercept. An intercept is the point where the line crosses one of the axes; the x-intercept is the point where it crosses the x-axis. Now, if you take a look at a graph, you'll see that the point where the line crosses the x-axis will always have 0 as its y coordinate!

So if you're looking for the x-intercept, by definition you're looking for the point where y=0. How do you do that? Well, simply by taking your equation, which was y=x+3, and setting y=0. If you solve 0=x+3, and subtract 3 from both sides, you have x=-3.

Hope it helps!
• Could you have an Absolute Value of 0.... If you had |0| it would be 0 but there is no way to have a negative 0 so would you ever write |0|. If so what would it be used for???
• the absolute value for zero is zero because zero is zero spaces away from zero on a number line.
• functions really confuse me so what is a good strategy that will help me understand it better?
• What are you having trouble with? Anything specific?
Well, here's an explanation that will hopefully clear things up.
Say you have a number |x|. Let's say for example, you plug in -1, you would always get that |-1| = 1. But what if you plug in 1? You get |1| = 1. Therefore, if you solve for |x|, it would have both a positive and a negative answer.

So, if you have a very simple equation, 2|x| = 1,
you would get,
|x| = 1/2
x = -1/2 or x = 1/2
The same sort of thing applies when you have an equation like
|x+5| = 1
x+5 = 1 or -1 because of the absolute value sign.

In essence, all you have to know to understand these sorts of equations is to that any term with an absolute value sign around has a single output (a positive number), but can have two different types of inputs for the same output (negative and positive).
• I have the problem |3x-2|=2*sqrt(x+8). The issue is I don't know where to start. Does the absolute value side have more weight and I therefore need to resolve the left side first? Or, does the square root side have more weight so I begin to resolve the right side of the equation? Is it possible to square an absolute value?
• Just like with the simpler problems, start by writing out the two equations you will be solving for (a positive and a negative output), Then solve each equation as you normally would.
• So, the absolute value of any negative or positive number would be positive?
• Yes. Unless you had this for example -|8| which would mean you solve the absolute value which is 8 and multiply it by negative one due to the negative dash. Hope this helped and good luck.
• What is the purpose of an absolute value equation?