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Absolute Value Equations - Concept
Solving for a variable in absolute value equations follows different rules than when we solve multi-step equations. When solving absolute value equations, most of the time we get more than one possible solution. Using absolute value equations, we are able to solve more complex concepts such as absolute values with inequalities, and graphs of absolute value inequalities with two variables.
Remember that when you're working with Absolute Value and try to solve equations, you have to keep in mind what Absolute Value means. And what Absolute Value means is distance away from zero. So like this is just a really basic problem that'll help you remember the concept. If the Absolute Value of x=5, what that means is that x is whatever number is five away from zero. So I draw little picture here's zero, x could be 1 2, 1 2 3 4 5 this way so x could equal to 5, and my other answer comes from when I move five in this direction 1 2 3 4 5 boom x=-5. Most of the time you're going to have two answers like that so you have to be aware when you're solving Absolute Value equations that you're probably going to have two answers and the way you solve the problems is that the first thing you do is do the mathematical solving techniques that I saw x the Absolute Value piece you want to get that Absolute Value piece all by itself before you do any solving equations.
The next thing you want to keep in mind is when you get to the bottom of your problem you're trying to figure how many answers you have, there's a couple little secrets you can remind yourself of. Most of the time you're going to get two answers. However, if you have something where your Absolute Value blah blah blah is equal to zero that means you're only going to have one solution and also if you get something where your Absolute Value blah blah blah is equal to some negative value negative, I'm just going to say negative a hundred, I made that up. Could be negative anything that means you're going to have no solution, because no number could be a negative distance away from zero remember Absolute Value means distance away from zero. It doesn't make sense to have a negative distance and that's why sometimes you're going to have no solution. It will make a lot more sense when two guys start doing a few problems. If you need help make sure you come back to this video and like review these little shortcuts about how you can tell how many answers you'll have.