Solving and Graphing Inequalities Joined by And or Or Classwork 1. Zara solved the inequality 18 < 3x 9 as shown below. Was she correct? 18 < 3x 9 27 < 3x 9 < x or x> 9 2. Consider the compound inequality 5 < xx < 4. a. Rewrite the inequality as a compound statement of inequality. b. Write a sentence describing the possible values of xx. x can be any number between -5 and 4. c. Graph the solution set on the number line below. d. Rewrite the inequality in interval notation. S.129
3. Consider the compound inequality 5 < 2xx + 1 < 4. a. Rewrite the inequality as a compound statement of inequality. b. Solve each inequality for xx. Then, write the solution to the compound inequality. c. Write a sentence describing the possible values of xx. x can be any number between -3 and 3/2. d. Graph the solution set on the number line below. 2. e. Write the solution in interval notation. 4. A friend of mine suggested I could solve the inequality as follows. Is she right? Explain your reasoning. 5 < 2xx + 1 < 4 5 1 < 2xx + 1 1 < 4 1 6 < 2xx < 3 3 < xx < 3 2 S.130
5. Given xx < 3 or xx > 1: a. What must be true in order for the compound inequality to be a true statement? x is any number less than -3 OR greater than -1. b. Write a sentence describing the possible values of xx. x can be any number less than -3 OR greater than -1. c. Graph the solution set on the number line below. 6. Given xx + 4 < 6 or 2xx + 2 < 6: a. Solve each inequality for xx. Then, write the solution to the compound inequality. b. Write a sentence describing the possible values of xx. x can be any number less than 2 OR greater than 4. c. Graph the solution set on the number line below. S.131
7. Solve ww 2 = 121, for ww. Graph the solution on a number line. 8. Solve ww 2 < 121, for ww. Graph the solution on a number line, and write the solution set as a compound inequality and in interval notation. 9. Solve ww 2 121, for ww. Graph the solution on a number line, and write the solution set as a compound inequality and in interval notation. 10. Use logical reasoning to solve (xx + 7) 2 = 121, for xx. Graph the solution on a number line. 11. Use your work from Exercise 10 to quickly graph the solution on a number line to each inequality below. i. (xx + 7) 2 < 121 ii. (xx + 7) 2 121 S.132
Homework Problem Set 1. Solve each compound inequality for xx, and graph the solution on a number line. Then write the solution in interval notation. A. xx + 6 < 8 and xx 1 > 1 B. 1 3 2xx 10 C. 5xx + 1 < 0 or 8 xx 5 D. 10 > 3xx 2 or xx = 4 2. Solve each compound inequality for xx, and graph the solution on a number line. A. xx 2 < 4 or xx 2 > 4 B. xx 2 4 and xx 2 4 3. 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. a. 1 + xx > 4 or 3xx 6 > 12 b. 1 + xx > 4 or 3xx 6 < 12 c. 1 + xx > 4 and 3xx 6 < 12 S.133
4. A. Solve the inequality 4xx + 8 > 2xx 10 or 1 xx 3 < 2 for xx, and graph the solution on a number line. 3 B. If the inequalities in Part A were joined by and instead of or, what would the solution set become? 5. A. Solve the inequality 7 3xx < 16 and xx + 12 < 8 for x, and graph the solution on a number line. B. If the inequalities in Part A were joined by or instead of and, what would the solution set become? 6. 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. S.134