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Chapter 2: Problem 90

Solve each inequality using a graphing utility. $$\frac{x+2}{x-3} \leq 2$$

Short Answer

Expert verified
To get the exact answer, the exact graph would be needed. But generally, the solution set will be the x-values for which the graph of \(y1 = \frac{x+2}{x-3}\) falls below or intersects with the line \(y2 = 2\), excluding any x-values that make the denominator of the fraction zero (since division by zero is undefined).

Step by step solution

01

Separate the inequality into two functions

Create two separate functions from the inequality, \(y1 = \frac{x+2}{x-3}\) and \(y2 = 2\).
02

Graph the functions

Using a graphing utility, graph the two functions \(y1\) and \(y2\). Identify any intersection points, these points show where \(y1 = y2\).
03

Identify the regions

After graphing, look at the sections of the x-axis where the graph of \(y1 (\frac{x+2}{x-3})\) is below or intersects with the horizontal line of \(y2 = 2\). These regions will give the possible x values that satisfy the inequality.
04

Formulate the solution

The solution will be the x-values that satisfy the original inequality. Be sure to include or exclude the intersection points, depending on whether the inequality is 'less than or equal to' or 'less than', respectively.

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Most popular questions from this chapter

What is a rational function?

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