- #1

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\left| {x - 9} \right| - \left| x \right| \ge 9

[/tex]

I started by rewriting it as:

[tex]

\left| {x - 9} \right| \ge 9 + \left| x \right|

[/tex]

Now, for any real numbers x and y,

[tex]

\left| {x + y} \right| \le \left| x \right| + \left| y \right|

[/tex]

According to that,

|x-9| cannot be greater than |x|+9, but it can be equal, if x and and 9 are of the same sign. The 9 is negative, so the x must also be negative, giving the solution [tex]

x \le 0

[/tex]

Why is it that the answer book says the answer is [tex]

x < 0[/tex]? Why is it excluding zero? Or is it just wrong?

Thanks,

Dan.