How do you write absolute value equations examples
If you answered no, then go on to step 3. This gives two possibilities: So this is why we end up with two different equations.
Absolute value function examples
Let's say we have the absolute value of x plus 2 is equal to 6. So just let me multiply this out, just so we have it in mx plus b form. Both with be solutions provided we solved the two equations correctly. Let's say I take the absolute value of negative 1. When you take the absolute value of a number, the result is always positive, even if the number itself is negative. Why does this work? And this is going to be the situation. This is due to the shape of the graph of the absolute value function.
Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets. Example 2 Solve each of the following.
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 let's think about two scenarios. Follow these steps to solve an absolute value equality which contains one absolute value: Isolate the absolute value on one side of the equation.
Now, to solve this one, add 5 to both sides of this equation. There is only one number that has the property and that is zero itself. If this whole thing evaluated to negative 6, you take the absolute value, you'd get 6.
Absolute value equations practice
This would be just changing the number on the right hand side of the equation. And just to kind of have it gel in your mind, that absolute value, you can kind of view it as a distance, you could rewrite this problem as the absolute value of x minus negative 2 is equal to 6. Likewise, there is no reason to think that we can only have one absolute value in the problem. So you kind of have this v-shaped function, this v-shaped graph, which is indicative of an absolute value function. Then you just solve these two equations. Let's do another one, and we'll do it in purple. When you take the absolute value of a number, the result is always positive, even if the number itself is negative. This means that any equation that has an absolute value in it has two possible solutions. There are two ways to define absolute value. And the graph, if we didn't have this constraint right here, would look something like this. Use this to determine when there are no solutions to an absolute value equation. So our solution, there's two x's that satisfy this equation. Summary Absolute value equations are always solved with the same steps: isolate the absolute value term and then write equations based on the definition of the absolute value. If you know you're taking the absolute value of a negative number, it's just like multiplying it by negative 1, because you're going to make it positive.
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