Advanced Math/Graph

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Expert: - 9/18/2010


Question
Sketch the graph of y=|x|,and hence or otherwise show that for all real numbers such that a>0, |x|<a is equivalent to -a<x<a

Answer

Graph
Hi Martin,
You can see from the attached image that for any line y = a (blue line), the value of |x| lies under the line for values of x between -a and a.
Mathematically looking at the inequality |x| < a, we know that;
|x| = x for all x > 0 i.e positive values
and |x| = -x for all negative x
Therefore, for x > 0, we have
x < a
and for x < 0,
-x < a
i.e x > -a
Combining the two solutions, we end up with
-a < x < a
just as we could have seen from the graph.

Regards

Ahmed Salami

Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I can as well help a good deal in Physics with most emphasis directed towards mechanics.

Experience

An engineering graduate. I have been doing maths and physics all my life.

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