BTGmoderatorDC wrote:Is -3*x^3 <= -3?
1) -3x<3
2) x <0
Source: GMAT Prep
$$ - 3{x^3}\,\,\mathop \leqslant \limits^? \,\, - 3\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( { - \frac{1}{3}} \right)} \,\,\,\,\,{x^3}\,\mathop \geqslant \limits^? \,\,1\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\root {3\,} \of {\,\,\,} } \,\,\,\boxed{\,\,x\,\mathop \geqslant \limits^? \,\,1\,\,}\,$$
$$\left( 1 \right)\,\,\, - 3x < 3\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\,x < 0\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle $$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
