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Chapter 3: Problem 91

Solve each inequality using a graphing utility. $$\frac{1}{x+1} \leq \frac{2}{x+4}$$

Short Answer

Expert verified
The solution to the inequality \( \frac{1}{x+1} \leq \frac{2}{x+4} \) can be determined by visual inspection of the graph. The exact solution depends on the graphical representation which might vary depending on the range and domain set on the graphing utility.

Step by step solution

01

Plot the Functions

First, put the inequality into equation form, we will plot \(y = \frac{1}{x+1}\) and \(y = \frac{2}{x+4}\). For this, enter the two functions to the graphing utility to generate their respective plots.
02

Identify Points of Intersection

Now look at the graph and identify where two functions intersect. Here, the points of intersection are the solutions of the equation. Depending on the graphing tool, simply hovering over the point might display the coordinates of the intersection point(s).
03

Determine Inequality Regions

Once we've located points of intersection, we need to determine the regions of the graph where \(y = \frac{1}{x+1}\) is less than or equal to \(y = \frac{2}{x+4}\). Observing the graph will give that information.

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Most popular questions from this chapter

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