Answer
(a) $x=3$
(b) $(3, +\infty)$
Work Step by Step
To solve the given equation graphically, perform the following steps:
(1) Treat each side of the equation as a function and graph them on the same coordinate plane.
Use a graphing calculator to graph $y=x-2$ (red graph) and $y=4-x$ (blue graph)
(refer to the image below for the graph)
(2) Identify the point/s where the graphs intersect
(a) The point/s where the two graphs intersect represents the instance where the $x-2$ is equal to $4-x$. The x-coordinate of this point is the solution to the given equation.
Notice that the graphs intersect at the point $(3, 1)$.
The x-coordinate of this point is $3$.
Thus, the solution to the given equation is $x=3$.
(b) The region where the graph of the function $y=x-2$ is higher than the graph of the function $y=4-x$ is the region where $x-2 \gt 4-x$.
Notice that the red graph ($y=x-2$) is higher than the blue graph ($y=4-x$) in the region $(3, +\infty)$. Since the inequality involves $\gt$, then the endpoint $3$ is not part of the solution set.
Thus, the solution to the given inequality is $(3, +\infty)$.
