Solving inequalities graphically

Dr. Wei-Chi Yang

Alternative way of solving problems for page 83.

  1. Solve MATH graphically.

    Solution: Let MATH and MATH Consider the graphs of $y=f(x)$ and $y=g(x)$ as follows: Notice that $y=g(x)$ is drawn in black and $y=f(x)$ is drawn in green. We are looking for interval(s) where $g(x)>f(x).$ We can see that there are two intersections which will give us the intervals we need. We are looking for the following intersections: $\{y=6-x,y=3-2x\}$ and $\{y=6-x,y=2x-3\}.$ It is easy to find these two intersections to be $x=-3$ and $x=3$ respectively and the answer for $g(x)>f(x)$ is when MATH
    addpage 83__15.png

  2. Solve MATH graphically.

    Solution: First we rewrite the inequality as follows:
    Now we define MATH and MATH and use the graphical approach we described above to find the interval(s) for which MATH We consider the graphs of $y=f(x)$ (black), $y=g(x)$ (green) and $y=h(x)$ (red) as follows: (Notice that these are basic graphs, which one can figure out easily by hand.) We leave the readers to find appropriate intersections by hand. The answer is MATH
    addpage 83__26.png

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