1003082605

Solve the following system of two inequalities. $$\begin{array}{rl}{\left(\frac{1}{2}\right)}^{x+1}-3{\left(\frac{1}{2}\right)}^{x+2}+\frac{1}{2}& \ge 0\\ 4^{x+2}-3\cdot 4^{x+1}& <1\end{array}$$