Answer
$[\frac{4}{3},\infty)$
Work Step by Step
We solve the inequality:
$\displaystyle \frac{x}{2}\geq 1-\frac{x}{4}$
$2x\geq 4*1-x$
$3x\geq 4$
$x\displaystyle \geq\frac{4}{3}$
Thus, the solution is the interval: $[\frac{4}{3},\infty)$