Answer
Set notation :- $\{x|x\geq \frac{4}{3}\}$
Interval notation :- $[\frac{4}{3},\infty )$.
The graph is shown below.
Work Step by Step
Multiply both sides by $4$.
$4\cdot \frac{x}{2} \geq 4\cdot (1- \frac{x}{4}) $
Simplify.
$2x \geq 4- x $
Add $x$ to both sides.
$2x+x \geq 4- x+x $
Simplify.
$3x \geq 4 $
Divide both sides by $3$.
$\dfrac{3x}{3}\geq \dfrac{4}{3} $
Simplify.
$x\geq \dfrac{4}{3} $
The solution set is $\{x|x\geq \frac{4}{3}\}$
or interval notation is $\left[\frac{4}{3},\infty\right)$.
To graph, use an open bracket at $\frac{4}{3}$ and shade the region to its right..
