Answer
(a) $\{ -\frac{5}{3} \}$
(b) $(-\infty, -\frac{5}{3})$
(c) $\{ 2 \}$
(d) $[2,\infty)$
(e) Refer to the attached image fir the graph.
Work Step by Step
Given $f(x)=3x+5$ and $g(x)=-2x+15$, we have:
(a) Let $f(x)=0$ or $3x+5=0$, thus $x=-\frac{5}{3}$ or $\{ -\frac{5}{3} \}$
(b) Let $f(x)\lt0$ or $3x+5\lt0$, thus $x\lt-\frac{5}{3}$ or $(-\infty, -\frac{5}{3})$
(c) Let $f(x)=g(x)$, we have $3x+5=-2x+15$, thus $x=2$ or $\{ 2 \}$
(d) Let $f(x)\ge g(x)$, we have $3x+5\ge -2x+15$, thus $x\ge2$ or $[2,\infty)$
(e) Use a graphing tool to graph the two functions.. The point that represents the solution to the equation $f(x)=g(x)$ is the point where the lines intersect, which is the point in part(c) -- is $(2,11)$.
