1. **Stating the problem:** We are given the inequality $x < 4y$ and want to understand its meaning and how to work with it. 2. **Understanding the inequality:** The inequality $x < 4y$ means that the value of $x$ is less than four times the value of $y$. 3. **Rearranging the inequality:** We can rewrite it to express $y$ in terms of $x$: $$x < 4y \implies \frac{x}{4} < y$$ This means $y$ must be greater than $\frac{x}{4}$. 4. **Graphical interpretation:** The boundary line is $y = \frac{x}{4}$. The inequality $y > \frac{x}{4}$ represents the region above this line. 5. **Summary:** The solution set to $x < 4y$ is all points $(x,y)$ where $y > \frac{x}{4}$. This inequality describes a half-plane in the coordinate plane.