Solve the inequality [tex](adsbygoogle = window.adsbygoogle || []).push({});

\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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rewriting inequality help

**Physics Forums | Science Articles, Homework Help, Discussion**