SOLUTION: What does the sign |x| means? What is the answer of x if it is |x-4|>3?

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Question 465561: What does the sign |x| means? What is the answer of x if it is |x-4|>3?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It's called "absolute value".
It means that whatever is inside
the bars, you ignore the minus if it
has a minus sign. Therefore:
+abs%28-10%29+=+10+
+abs%2810%29+=+10+
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You have:
+abs%28x-4%29+%3E+3+
Try +x+=+4+, then
+abs%284-4%29+%3E+3+
+0+%3E+3+ not true
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If +0+%3C+x+%3C+1+,
+abs%28+.9+-+4+%29+%3E+3+
+abs%28-3.1%29+%3E+3+
+3.1+%3E+3+ true
-------------------------
Try +x+=+7+
+abs%287+-+4%29+%3E+3+
+3+%3E+3+ also not true
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But if +x+%3E+7+,
+abs%287.1+-+4%29+%3E+3+
+3.1+%3E+3+ true
-------------------------
If +x+%3C=+0+, then
+abs%28-.1+-+4%29+%3E+3+
+4.1+%3E+3+ true
-------------------------
What it boils down to is,
there are 2 ranges for x
that make the inequality true:
+x+%3C+1+
and
+x+%3E+7+
Anything between and including
1 and 7 fails
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Hope this helps