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Chapter 9: Problem 71
What is a system of linear inequalities?
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Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's mamual for your graphing utility that describes how to shade a region. Then use your graphing unility to graph the inequalities. $$y \geq \frac{2}{3} x-2$$
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I'm considering the compound inequality \(x<8\) and \(x \geq 8,\) so the solution set is \(\varnothing\)
Solve each inequality using a graphing utility. Graph each of the three parts of the inequality separately in the same viewing rectangle. The solution set consists of all values of \(x\) for which the graph of the linear function in the middle lies between the graphs of the constant functions on the left and the right. $$1 \leq 4 x-7 \leq 3$$
Solve each inequality using a graphing utility. Graph each of the three parts of the inequality separately in the same viewing rectangle. The solution set consists of all values of \(x\) for which the graph of the linear function in the middle lies between the graphs of the constant functions on the left and the right. $$-1<\frac{x+4}{2}<3$$
Graph the solution set of each system of inequalities or indicate that the system has no solution.. \left\\{\begin{array}{l}x \geq 0 \\\y \geq 0 \\\2 x+y \leq 4 \\\2 x-3 y \leq 6\end{array}\right.
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