1. The problem is to solve the inequality $4x + 1 < -x + 6$ graphically. 2. We graph the functions $f(x) = 4x + 1$ and $g(x) = -x + 6$ on the same set of axes. 3. The inequality $4x + 1 < -x + 6$ means we want to find the values of $x$ where the graph of $f$ is less than the graph of $g$. 4. To solve graphically, find the intersection point of $f(x)$ and $g(x)$ by setting $4x + 1 = -x + 6$. 5. Solve for $x$: $$4x + 1 = -x + 6$$ $$4x + x = 6 - 1$$ $$5x = 5$$ $$x = 1$$ 6. At $x=1$, the graphs intersect. For values of $x$ less than 1, check if $f(x) < g(x)$. 7. Test $x=0$: $f(0) = 1$, $g(0) = 6$, and $1 < 6$ is true. 8. For $x > 1$, test $x=2$: $f(2) = 9$, $g(2) = 4$, and $9 < 4$ is false. 9. Therefore, the solution to the inequality is $x < 1$. Final answer: $$x < 1$$