1. **State the problem:** We are given two expressions representing parallel lines: $15x + 4$ and $20x + 1$. We want to find the value of $x$ for which these two lines are equal, i.e., solve the equation $15x + 4 = 20x + 1$. 2. **Write the equation:** $$15x + 4 = 20x + 1$$ 3. **Isolate the variable $x$:** Subtract $15x$ from both sides: $$\cancel{15x} + 4 = 20x - \cancel{15x} + 1$$ which simplifies to $$4 = 5x + 1$$ 4. **Subtract 1 from both sides:** $$4 - 1 = 5x + 1 - 1$$ which simplifies to $$3 = 5x$$ 5. **Divide both sides by 5 to solve for $x$:** $$\frac{3}{\cancel{5}} = x \cdot \frac{\cancel{5}}{5}$$ which simplifies to $$x = \frac{3}{5}$$ 6. **Final answer:** The value of $x$ that makes the two lines equal is $$x = \frac{3}{5}$$ This means the two expressions are equal when $x$ is $0.6$.