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Chapter 1: Problem 140
Explain why \(|x|<-4\) has no solution.
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Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \text { for } R_{1}$$
One of the best ways to learn how to solve a word problem in algebra is to design word problems of your own. Creating a word problem makes you very aware of precisely how much information is needed to solve the problem. You must also focus on the best way to present information to a reader and on how much information to give. As you write your problem, you gain skills that will help you solve problems created by others. The group should design five different word problems that can be solved using linear equations. All of the problems should be on different topics. For example, the group should not have more than one problem on simple interest. The group should turn in both the problems and their algebraic solutions.
In Exercises \(127-130,\) solve each equation by the method of your choice. $$ \frac{1}{x^{2}-3 x+2}=\frac{1}{x+2}+\frac{5}{x^{2}-4} $$
Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.
Things did not go quite as planned. You invested \(\$ 12,000\), part of it in stock that paid \(14 \%\) annual interest. However, the rest of the money suffered a \(6 \%\) loss. If the total annual income from both investments was \(\$ 680,\) how much was invested at each rate?
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