C. Graph the solution to possibilities for Sharmara s number and give the solution in interval notation.

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Graph the solution to possibilities for Sharmara s number and give the solution in interval notation. S.78 2. Benjamin is also thinking of a number. A.

1 Homework Problem Set Sample Solutions S.77 Homework Problem Set 1. Shamara is thinking of a number. A. Could Shamara be thinking of 8? Explain. No, if Shamara thought of 8, the answer would equal 2. B. How is Sharmara s statement written using algebra? 10 x > 2 C. Graph the solution to possibilities for Sharmara s number and give the solution in interval notation. S Benjamin is also thinking of a number. A. Write Benjamin s statement using algebra. 4x > 10 B. Graph the solution to possibilities for Benjamin s number and give the solution in interval notation. Unit 3: Solving Equations & Inequalities 131

2 Draw a graph for each inequality and give the solution in interval notation. [source: Kuta software] 3. n < n < 5 5. r > 2 6. r < x > > v 9. 5 > -b 10. a > 2 Note: Problem 9 is a bit different and students may struggle with this one. It is a good transition into solving inequalities in the next lesson when you have to multiply or divide by a negative number in an inequality. Unit 3: Solving Equations & Inequalities 132

3 S.79 Write an inequality for each graph and give the solution in interval notation. [source: Kuta software] 11. x < 5 (-, 5] 12. x < -1 (-, -1) 13. x > -1 (-1, ) 14. x < -5 (-, -5) 15. x < 2 (-, 2) 16. x < -5 (-, -5] Use mental math to solve and graph each inequality. hen and give the solution in interval notation > x 7-5 > x (-, -5) r > 4 r > 5 [5, ) 19. n 6 < 14 n < -8 (-, -8] 20. b 7 < 12 b < -5 (-,-5) Unit 3: Solving Equations & Inequalities 133

4 Error Note: Problem 21 is missing the inequality. he problem should read a 17 > a 17 > 16 a > 1 (1, ) x < 0 x < -15 (-, -15] S v < 9 v < -12 (-, -12] > n 6 n < 14 (-, 14] n k 25. > 3 n > 9 (9, ) 26. < 4 k < -16 (-, -16) n > 84 n > 7 [7, ) > 10 + b b < -12 (-, -12) Unit 3: Solving Equations & Inequalities 134

5 Inequality Statement x > x 10 > x 31. 2x > 10 x 32. < 2 5 x 33. > 5 2 Simplified Inequality Statement If you subtract a number from ten, then your answer will be greater than ten. If you subtract ten from a number, your greater than the number. If you multiply two greater If you divide a number by five, your less than two. If you divide a number by two, your greater than 5. Interval Notation of Solution the number is negative. here are no values for which this is true. the number is greater than five. the number is less than ten. the number is greater Graph of Solution Unit 3: Solving Equations & Inequalities 135

6 Card Matching (one set per student) here are no values for which this is true. If you subtract two from a number, your than eight. greater than one or when the number is negative. If you divide ten If you add a number to ten, your more If you multiply ten greater than the number. less If you add ten to a number, your than the number. here are no values for which this is true. If you subtract two from a number, your than eight. greater than one or when the number is negative. If you divide ten If you add a number to ten, your more If you multiply ten greater than the number. less If you add ten to a number, your than the number. Unit 3: Solving Equations & Inequalities 136

Lesson 9: Introduction to Inequalities

Lesson 9: Introduction to Inequalities Opening Exercise - [adapted from MARS Evaluating Statements About Number Operations] 1. Abigail is thinking of a number. A. Could Abigail be thinking of 8? Explain your answer. B. What numbers could she