Answer
$$\color{blue}{[15,\infty)}$$
Work Step by Step
Remember that the break even point is where the revenue, $R$ is greater than or equal to the costs, $C$, or simply:
$$R\geq{C}$$
Simply plug in the values and work the inequality
$500x\geq{100x+6000}$
subtract $100x$ from both sides
$400x\geq{6000}$
divide both sides by $400$
$400x\geq{6000}$
$x\geq{15}$
The break even point is $\color{blue}{[15,\infty)}$
