Answer
$\displaystyle \left\{x\ |\ x \lt -\frac{1}{2} \right\}$ or $\displaystyle \left(-\infty, \ -\frac{1}{2}\right)$
Work Step by Step
$(4x+2)^{-1}=\displaystyle \frac{1}{4x+2}$
If this fraction is negative, then
its denominator is negative:
$ 4x+2 \lt 0\qquad$ ... add $-2$
$ 4x \lt -2 \qquad$... multiply with $\displaystyle \frac{1}{4}$
$x \lt -\displaystyle \frac{1}{2}$
Solution set: $\displaystyle \left\{x\ |\ x \lt -\frac{1}{2} \right\}$ or $\displaystyle \left(-\infty, \ -\frac{1}{2}\right)$
