Answer:
[tex]\large\boxed{x\geq9\to x\in\left[9,\ \infty\right)}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{2}x+\dfrac{3}{4}\geq5\dfrac{1}{4}\qquad\text{convert the mixed number to the improper fraction}\\\\\dfrac{1}{2}x+\dfrac{3}{4}\geq\dfrac{5\cdot4+1}{4}\\\\\dfrac{1}{2}x+\dfrac{3}{4}\geq\dfrac{21}{4}\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup^2\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x+4\!\!\!\!\diagup^1\cdot\dfrac{3}{4\!\!\!\!\diagup_1}\geq4\!\!\!\!\diagup^1\cdot\dfrac{21}{4\!\!\!\!\diagup_1}\\\\2x+3\geq21\qquad\text{subtract 3 from both sides}\\\\2x\geq18\qquad\text{divide both sides by 2}\\\\x\geq9[/tex]
<, > - open circle
≤, ≥ - closed circle
<, ≤ - draw the line to the left
>, ≥ - draw the line to the right
