1.1 - CHAPTER 1 EXERCISES 1.1 page 10 1 The statement is...

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CHAPTER 1 EXERCISES 1.1, page 10 1. The statement is false because -3 is greater than -20. (See the number line that follows). 2. The statement is true because -5 is equal to -5. 3. The statement is false because 2/3 [which is equal to (4/6)] is less than 5/6. 4. The statement is false because -5/6 (which is -10/12) is greater than -11/12. 5. The interval (3,6) is shown on the number line that follows. Note that this is an open interval indicated by ( and ) . 6. The interval (-2,5] is shown on the number line that follows. 7. The interval [-1,4) is shown on the number line that follows. Note that this is a half-open interval indicated by [ (closed) and ) (open). 8. The closed interval [-6/5, -1/2] is shown on the number line that follows. 1 Preliminaries 1

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9. The infinite interval (0, ) is shown on the number line that follows. 10. The infinite interval (- ,5] is shown in the number line that follows. 11. First, 2 x + 4 < 8 ( Add -4 to each side of the inequality .) Next, 2 x < 4 ( Multiply each side of the inequality by 1/2 ) and x < 2. We write this in interval notation as ( , ). −∞ 2 12. -6 > 4 + 5 x -6 - 4 > 5 x -10 > 5 x -2 > x or x < -2. We write this in interval notation as (- ,-2). 13. We are given the inequality -4 x > 20. Then x < -5. ( Multiply both sides of the inequality by -1/4 and reverse the sign of the inequality .) We write this in interval notation as (- ,-5]. 14. -12 < -3 x 4 > x , or x < 4. We write this in interval notation as (- ,4]. 15. We are given the inequality -6 < x - 2 < 4. First -6 + 2 < x < 4 + 2 ( Add +2 to each member of the inequality .) and -4 < x < 6, so the solution set is the open interval (-4,6). 16. We add -1 to each member of the given double inequality 0 < x + 1 < 4 to obtain -1 < x < 3, and the solution set is [-1,3]. 1 Preliminaries 2
17. We want to find the values of x that satisfy the inequalities x + 1 > 4 or x + 2 < -1. Adding -1 to both sides of the first inequality, we obtain x + 1 - 1 > 4 - 1, or x > 3. Similarly, adding -2 to both sides of the second inequality, we obtain x + 2 - 2 < -1 - 2, or x < -3. Therefore, the solution set is (- ,-3) (3, ). 18. We want to find the values of x that satisfy the inequalities x + 1 > 2 or x - 1 < -2. Solving these inequalities, we find that x > 1 or x < -1, and the solution set is (- ,-1) (1, ). 19. We want to find the values of x that satisfy the inequalities x + 3 > 1 and x - 2 < 1. Adding -3 to both sides of the first inequality, we obtain x + 3 - 3 > 1 - 3, or x > -2.

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1.1 - CHAPTER 1 EXERCISES 1.1 page 10 1 The statement is...

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