Nevernevergiveup wrote:

Is \(x > 0\)?

1. \(x^2 = 9x\)

2. \(|x| = -x\)

\(x\,\,\mathop > \limits^? \,\,0\)

\(\left( 1 \right)\,\,{x^2} = 9x\,\,\,\, \Leftrightarrow \,\,\,\,x\left( {x - 9} \right) = 0\,\,\,\, \Leftrightarrow \,\,\,\,\left\{ \matrix{

\,x = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr

\,\,\,{\rm{OR}} \hfill \cr

\,x = 9\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.\)

\(\left( 2 \right)\,\,\,\left| x \right| = - x\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x \le 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)

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