Explain the steps in solving the following absolute value equation. 2|x−2|=12. (There should be two answers)

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Explain the steps in solving the following absolute value equation. 2|x−2|=12. (There should be two answers)

Mathematics
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Hello @GalacticPlunder :) Sorry for the slightly late response :-/ first we should try to get the absolute values alone on one side so I suggest dividing both sides by 2 first :) can you do that?
So it world be: x-2 = 6. Then if I add two it would be x = 8 right? My teacher said there should be two answers though. I don't know what that means :/
it's just saying that for example if |x| = 2 then if can be split up into two equations: x = 2 and x = -2 this way: |x - 2| = 6 can be split up into x - 2 = 6 and x - 2 = -6

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Other answers:

How can it be split into two equations?
the absolute value means that anything inside it comes out as a positive value absolute value of +2 = | 2 | = 2 and | - 2 | = 2 so if a "variable" is in the absolute value, there can be two answers (one for the positive/normal idea, and one for the negative idea)
ohhhh Thanks so much!
Could you help me with another?
sure thing :)
How do you show where an inequality is true on a number line?
Also this was added: "let's say you had a solution of x>2. How would you show this on a number line"
|dw:1439315529603:dw|
you would start on \(2\) :P then if the inequality > < thing has a line under it, it would mean \(include~the~number\) and be a dark circle (not the hollow one I drew) if the wider part of the > is facing the variable like \(x>\) that means you should shade the numbers Bigger than the given number
Thanks! Could you help me with one last problem?
of course :)
What is a literal equation? How is solving a literal equation different from solving a one- or two-step equation?
A literal equation is an equation that is made up of all letters [variables] for example: \(A=b*h\) The difference between a one- or two-step equation and a literal equation is that in a one- or two-step equation, the aim (usually) is to get a numerical answer (a number as the answer). But for a literal equation, solving for a variable simply rearranges the original equation. Sorry if that's a little confusing, here's a link about literal equations that describes it better :) http://www.purplemath.com/modules/solvelit.htm
Awesome! Thank you so much!
Glad I could help :)

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