Lesson 11 S.95. A. Rewrite the inequality as a compound sentence and in interval notation. B. Graph the inequality on a number line.

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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 00 < xx < 33. A. Rewrite the inequality as a compound sentence and in interval notation. xx > 00 and xx < 33 (0, 3) 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. xx can be any value between 00 and 33, which includes the integer values of 11 and 22 as well as non-integer values. he set of numbers between 00 and 33 is infinite. D. What are the largest and smallest possible values for xx? Explain. here is no absolute largest or absolute smallest value for xx. xx can be infinitely close to 00 or to 33 but cannot equal either value. E. If the inequality is changed to 00 xx 33, then what are the largest and smallest possible values for xx? In this case, we can define the absolute maximum value to be 33 and the absolute minimum value to be 00. Unit 3: Solving Equations & Inequalities 159

2 S.96 Write a compound inequality for each graph. hen write it in interval notation xx < 11 or xx 33 (-, 1) or [3, ) xx < 22 or xx > 22, which can be written as xx 22 (-, 2) or (2, ) Write a single or compound inequality for each scenario. hen write it in interval notation. 4. he scores on the last test ranged from 6655% to %. xx = scores on last test 6655 xx [65, 100] 5. o ride the roller coaster, one must be at least 44 feet tall. xx = height (in feet) to ride the roller coaster xx 44 [4, ) In reality there is probably a maximum height too. 6. Unsafe body temperatures are those lower than 9966 FF or above FF. xx = body temperature (in degrees Fahrenheit) that are unsafe xx < 9966 or xx > [0, 96) or (104, ) Again, there are probably upper and lower limits that are not addressed in this problem. Unit 3: Solving Equations & Inequalities 160

3 Graph the solution(s) to each of the following on a number line. 7. xx 88 or xx (xx 66) = 33 or 55 xx = xx < 99 and xx > xx + 55 < 77 or xx = 22 S xx 44 = 00 and 33xx + 66 = xx < 55 and xx 00 Unit 3: Solving Equations & Inequalities 161

4 Solve each compound inequality for xx, and graph the solution on a number line. hen write the solution in interval notation. M. xx + 66 < 88 and xx 11 > 11 xx < 22 and xx > < xx < 22 (0, 2) N xx 1100 xx 77 and xx xx 22 [-7/2, 2] O. 55xx + 11 < 00 or 88 xx 55 xx < or xx 1133 (-, -1/5) or [13, ) P > 33xx 22 or xx = 44 xx < 44 or xx = 44 xx 44 (-, 4] Solve each compound inequality for xx, and graph the solution on a number line. 17. xx 22 < 44 or xx 22 > 44 xx < 66 or xx > 66 xx 66 (-, 6) or (6, ) 18. xx and xx xx = 66 Unit 3: Solving Equations & Inequalities 162

5 S.98 Solve each compound inequality for xx, 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 xx > 44 or 33xx 66 > 1122 xx > xx > 44 or 33xx 66 < 1122 xx can be any real number. U xx > 44 and 33xx 66 < 1122 xx > 33 and xx < 22 No solution (empty set) since there are no numbers that satisfy both statements 22. A. Solve the inequality 44xx + 88 > 22xx 1100 or 11 xx 33 < 22 for xx, and graph the solution on a number line. 33 xx > 99 or xx < 1155 all real numbers B. If the inequalities in Part A were joined by and instead of or, what would the solution set become? 99 < xx < 1155 S A. Solve the inequality 77 33xx < 1166 and xx < 88 for x, and graph the solution on a number line. xx > 33 and xx < 2200 no solution B. If the inequalities in Part A were joined by or instead of and, what would the solution set become? xx > 33 or xx < 2200 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. For both of these questions we are looking for student understanding of or and and. he only ones that work are trivial cases where the answer to both is the empty set or 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 < 00 or rue, the first statement is true and we have a disjunction (only one needs to be true). S.100 Solve each system, and graph the solution on a number line. 27. xx 99 = 00 or xx = xx 88 = 2233 or xx + 11 = 1100 {9, 15} {-3, -11} Graph the solution set to each compound inequality on a number line. 29. xx < 88 or xx > < xx 1100 Unit 3: Solving Equations & Inequalities 164

7 Write a compound inequality for each graph xx 44 xx < 44 or xx > A poll shows that a candidate is projected to receive 5577% of the votes. If the margin for error is plus or minus 33%, write a compound inequality for the percentage of votes the candidate can expect to get. Let xx = percentage of votes xx 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 xx = temperatures (in degrees Fahrenheit) for which mercury is nonliquid. xx < 3388 or xx > 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. Unit 3: Solving Equations & Inequalities 165