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Chapter 1: Problem 16
After a \(30 \%\) reduction, you purchase a dictionary for \(\$ 30.80 .\) What was the dictionary's price before the reduction?
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Each group member should research one situation that provides two different pricing options. These can involve areas such as public transportation options (with or without discount passes), cellphone plans, long-distance telephone plans, or anything of interest. Be sure to bring in all the details for each option. At a second group meeting, select the two pricing situations that are most interesting and relevant. Using each situation, write a word problem about selecting the better of the two options. The word problem should be one that can be solved using a linear inequality. The group should turn in the two problems and their solutions.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I prefer interval notation over set-builder notation because it takes less space to write solution sets.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. What's wrong with this argument? Suppose \(x\) and \(y\) represent two real numbers, where \(x>y .\) $$ \begin{aligned} 2 &>1 \\ 2(y-x) &>1(y-x) \\ 2 y-2 x &>y-x \\ y-2 x &>-x \\ y &>x \end{aligned} $$ The final inequality, \(y>x,\) is impossible because we were initially given \(x>y\)
Find all values of \(x\) satisfying the given conditions. $$ y_{1}=x-3, y_{2}=x+8, \text { and } y_{1} y_{2}=-30 $$
Solve equation by the method of your choice. $$ \sqrt{2} x^{2}+3 x-2 \sqrt{2}=0 $$
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