Problem

Figure 1 shows a line $l_1$ with equation $2y=x$ and a curve $C$ with equation

$$\begin{align*} y=2x-\frac18x^2. \end{align*}$$

The region $R$, shown unshaded in Figure 1, is bounded by the line $l_1$, the curve $C$ and a line $l_2$.

Figure 1

Given that $l_2$ is parallel to the $y$-axis and passes through the intercept of $C$ with the positive $x$-axis, identify the inequalities that define $R$.