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Chapter 2: Problem 86

Solve each inequality using a graphing utility. $$x^{2}+3 x-10>0$$

Short Answer

Expert verified
The solution to the inequality \(x^{2}+3x-10>0\) will be the x-values of the plotted graph that are above the x-axis. The exact values depend on the plotted graph.

Step by step solution

01

- Write the inequality

We write down the inequality that we're going to work with, which is \(x^{2}+3x-10>0\).
02

- Plot the quadratic function

Next, we plot the function \(y = x^{2}+3x-10\). This is a graph of a parabola as the function in question is a quadratic function.
03

- Identify the solutions

The solutions to the inequality \(x^{2}+3x-10>0\) are all x-values where the graph lies above the x-axis. In other words, they are values for which y > 0. If we look at the graph, we can draw a horizontal line at y=0 and see where the graph of our quadratic function is above this line. These x-values will be our solutions. The range of these x-values forms an interval, which represents the solution set to our inequality.

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Most popular questions from this chapter

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{3}-1}{x^{2}-9}$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$(x)=\frac{1}{(x+2)^{2}}$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{(x-3)^{2}}+2$$

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$\frac{1}{(x-2)^{2}}>0$$

Solve each inequality using a graphing utility. $$x^{3}+x^{2}-4 x-4>0$$
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