Answer:
[tex]\large\boxed{x\geq-\dfrac{4}{3};\ y\geq5}[/tex]
Step-by-step explanation:
We know:
[tex]\sqrt{a}=b\ for\ a\geq0\ adn\ b\geq0[/tex]
We have
[tex]y=2\sqrt{3x+4}+5[/tex]
Therefore
[tex]3x+4\geq0[/tex] subtract 4 from both sides
[tex]3x\geq-4[/tex] divide both sides by 3
[tex]x\geq-\dfrac{4}{3}[/tex]
[tex]\sqrt{3x+4}\geq0[/tex] multiply both sides by 2
[tex]2\sqrt{3x+4}\geq0[/tex] add 5 to both sides
[tex]2\sqrt{3x+4}+5\geq5\to y\geq5[/tex]
