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Chapter 1: Problem 86
Evaluate \(x^{2}-x\) for the value of \(x\) satisfying \(2(x-6)=3 x+2(2 x-1)\)
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The formula $$1-\frac{1}{4^{x}+26}$$ models the percentage of U.S. households with an interfaith marriage, \(I, x\) years after \(1988 .\) The formula $$N-\frac{1}{4} x+6$$ models the percentage of U.S households in which a person of faith is married to someone with no religion, \(N, x\) years after \(\overline{l 9} 88\). Use these models to solve. a. In which years will more than \(34 \%\) of U.S. households. have an interfaith marriage? b. In which years will more than \(15 \%\) of U.S. households have a person of faith married to someone with no religion? c. Based on your answers to parts (a) and (b), in which years will more than \(34 \%\) of households have an interfaith marriage and more than \(15 \%\) have a faith/no religion marriage? d. Based on your answers to parts (a) and (b), in which years will more than \(34 \%\) of households have an interfaith marriage or more than \(15 \%\) have a faith/no religion marriage?
Solve absolute value inequality. \(4<|2-x|\)
Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88 . There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90 . a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.
Solve absolute value inequality. \(|x-1| \leq 2\)
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.
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