Problem
Suppose that $f(x)=5 x-1$ and $g(x)=-4 x+8$ (a) Solve $f(x)=0$. (b) Solve $f(x)>0$. (c) Solve $f(x)=g(x)$. (d) Solve $f(x) \leq g(x)$. (e) Graph $y=f(x)$ and $y=g(x)$ and find the point that represents the solution to the equation $f(x)=g(x)$. (a) For what value of $x$ does $f(x)=0$ ? \[ x= \] (Type an integer or a simplified fraction.)
Solution
Step 1 ：Set the function $f(x)=5x-1$ equal to zero: $5x-1=0$
Step 2 ：Add 1 to both sides of the equation: $5x=1$
Step 3 ：Divide both sides of the equation by 5 to solve for x: $x=\frac{1}{5}$
Step 4 ：The value of $x$ that makes $f(x)=0$ is $\boxed{\frac{1}{5}}$
