write an absolute value epuation that has 2 and 6 as solutions

Question

anonymous · Answer

Welcome to OpenStudy, @brenna00 ! If you have any questions about the site and how to get around it, don't hesitate to ask.

First things first for this question: Do you know what an absolute value is?

anonymous · Answer

well I know what one looks like but I don't know the definition

anonymous · Answer

basically it means that instead of looking at it as positive or negative, you look at how far AWAY it is from 0. So the absolute value of -3 is just 3. 
Does that make sense?

anonymous · Answer

yes

anonymous · Answer

So if you apply that to equations, it would be like this:
$$\left| x-10 \right| =6$$
Solution 1: x-10=6, so x=16
Solution 2: x-10 = -6, so x =4

The two solutions in that case are 4 and 16. 
In this case, you need to find two equations whose solutions are 2 and 6.

anonymous · Answer

(basically you take the absolute value expression and set it equal to a negative number and a positive number, and it gives you two different answers)

anonymous · Answer

That's fair ;) Let me see if i can help

anonymous · Answer

How about $$\left| x-4 \right| = 2$$ ? Would that work?

anonymous · Answer

yes it works

anonymous · Answer

thank you

anonymous · Answer

no problem! :)