Lesson 11. S Consider the inequality < <. A. Rewrite the inequality as a compound sentence and in interval notation. > and <

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1 Homework Problem Set Sample Solutions Note: here are too many homework problems to be done in one night. Consider using some of the problems in a review game before the unit test. S Consider the inequality < <. A. Rewrite the inequality as a compound sentence and in interval notation. > and < B. Graph the inequality on a number line. C. How many solutions are there to the inequality? Explain. here are an infinite number of solutions. and, and as well as non- ues. he set of numbers between and is infinite. D. What are the largest and smallest possible values for? Explain.. can be infinitely close to or to but cannot equal eithe E. If the inequality is changed to, then what are the largest and smallest possible values for? and the. : And or Or Unit 3: Solving Equations & Inequalities 159

2 S.96 Write a compound inequality for each graph. hen write it in interval notation < or (- < or >, which can be written as (- Write a single or compound inequality for each scenario. hen write it in interval notation. 4. he scores on the last test ranged from % to %. = scores on last test 5. o ride the roller coaster, one must be at least feet tall. = height (in feet) to ride the roller coaster 6. Unsafe body temperatures are those lower than or above. = body temperature (in degrees Fahrenheit) that are unsafe < or > addressed in this problem. : And or Or Unit 3: Solving Equations & Inequalities 160

3 Graph the solution(s) to each of the following on a number line. 7. or 8. ( )= or = 9. < and > < or = S = and + = 12. < and : And or Or Unit 3: Solving Equations & Inequalities 161

4 Solve each compound inequality for, and graph the solution on a number line. hen write the solution in interval notation. M. + < and > < and > < < (0, 2) N. and [-7/2, 2] O. + < or < or (- - P. > or = < or = (- Solve each compound inequality for, and graph the solution on a number line. 17. < or > < or > (- 18. and = : And or Or Unit 3: Solving Equations & Inequalities 162

5 S.98 Solve each compound inequality for, and graph the solution on a number line. Pay careful attention to the inequality symbols and the and or or statements as you work. S. + > or > >. + > or < can be any real number. U. + > and < > and < No solution (empty set) since there are no numbers that satisfy both statements 22. A. Solve the inequality + > or < for, and graph the solution on a number line. > or < all real numbers B. If the inequalities in Part A were joined by and instead of or, what would the solution set become? < < S A. Solve the inequality < and + < for x, and graph the solution on a number line. > and < no solution B. If the inequalities in Part A were joined by or instead of and, what would the solution set become? > or < : And or Or Unit 3: Solving Equations & Inequalities 163

6 24. A. Is it possible to write a problem separated by or that has no solution? Explain or give an example. B. Is it possible to have a problem separated by and that has a solution set consisting of all real numbers? Explain or give an example. the answer to both is all real numbers. Determine if each sentence is true or false. Explain your reasoning and < rue, since both statements are true. 26. < or + rue, the first statement is true one needs to be true). S.100 Solve each system, and graph the solution on a number line. 27. = or + = 28. = or + = {9, 15} {- - Graph the solution set to each compound inequality on a number line. 29. < or > 30. < : And or Or Unit 3: Solving Equations & Inequalities 164

7 Write a compound inequality for each graph < or > 33. A poll shows that a candidate is projected to receive % of the votes. If the margin for error is plus or minus %, write a compound inequality for the percentage of votes the candidate can expect to get. Let = 34. Mercury is one of only two elements that are liquid at room temperature. Mercury is non-liquid for temperatures less than. or greater than.. Write a compound inequality for the temperatures at which mercury is nonliquid. Let = temperatures (in degrees Fahrenheit) for which mercury is nonliquid. < or >. Fun Fact: he other element that is liquid at room temperature is bromine. Students could be asked to look up the temperatures at which bromine is non-liquid and write a similar compound inequality. : And or Or Unit 3: Solving Equations & Inequalities 165