How is this solved?
$\displaystyle
(x-1) \left( x+\frac{1}{2} \right) \geq 0
$
Also, I have no idea what I entered wrong with Latex.
The "escape" is a back-slash, not a forward slash. I think you meant the following...?
$\displaystyle (x\, -\, 1)\left(x\, +\, \frac{1}{2}\right)\, \geq\, 0$
If so, note that this is a positive quadratic, so you know what shape it has. Look at the factors to determine where the graph crosses the axis, and then use your knowledge of the shape of the graph to determine where the graph is at or above the x-axis.