Example 1

We consider the revenue function $R(x)=10x$ and the cost function $C(x)=8x+30$ and we determine the break-even point.

This implies the following:
$$\begin{align} R(x)  = C(x) & \Leftrightarrow 10x=8x+30\\ & \Leftrightarrow 2x=30\\ & \Leftrightarrow x=15. \end{align}$$

Hence, the break-even point is $x=15$.