# For any x, |x−7|=?

Question:Can someone explain this to me:
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For any x, |x−7|=
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i know it = |7−x|
i just don't know why...websites help to

|x−7|=

that means that (x-7) can be a positive number
. or (x-7) can be a negative number...

BUT when you take the absolute value of the POS or NEG number, both will result in the same POS number

so... let's say x-7 is the first quantity... POS

then... |x−7|= |x| + |-7| = x + 7

but let's say that x-7 is a negative number. if you had |x|= 9, then x = 9 or x = -9 or you can think of it as x = POS "quantity" or x = NEG quantity...

Our "blah" is (x-7) . which can be either POS blah ... i.e. +(x-7) which we already considered.
. or NEG blah... i.e. -(x-7) = -x + 7 = 7 - x.

Now... when you take |-x+7| or |7-x| =... you get |7| +|-x| = 7 + x

Since you had |x−7|= |x| + |-7| = x + 7

. and now found out |-(x-7)| = |-x+7| = |7-x| = |7| +|-x| = 7 + x

because they both resulted in the SAME "POS quantity/number" of (7+x) like I said that it would at the beginning. that automatically means that ...|x-7| = |7-x| because they both result in (7 + x) after taking the absolute values of (x-7) and (7-x)

So... no matter what you values of x are... any value of x, this relationship will be true... |x-7| = |7-x|
7 less then x
Well i don't understand what for any x means, but i'm guessing ur asking {x-7} so its just the x subtracting the 7 away from it.

For example x=1 x-7= 1-7= -6

OR

x=9 x-7= 9-7= 2

Hope it helps and sry if it doesn't!
When solving absolute values, you want to split the problem into 2 cases. When splitting the prob, you are finding the answer based on the positive aspect and the negative aspect of an absolute value. Recall that absolute values are solved based on making the equation like it is (positive) and then another equation (making it negative), that's why on a graph it's shaped like a V. You make it into regular computations:

1) x-7=x-7
2) -(x-7)= -x+7

1) is explanatory on what it equals. x-7
2) you can distribute the - sign, which makes it -x+7. This is your answer. Distribution: -1*x= -x. and -1*-7=+7

Look at the link's 1st & 2nd problem. See how they find the answer splitting the problem up by finding the positive side and the negative side. Since one of the answers is 7-x, putting absolute values around it just clarifies that it doesn't equal -(7-x).

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