35. 36.
37. 38.
- 10 a
1
5
x+ 2 b 610 a
1
5
8 a x+ 1 b
1
2
x+ 3 b 68 a
1
2
x- 1 b
312 x- 42 - 4 x 62 x+ 3 714 - x 2 + 5 x 62116 - x 2
3
5
1 t- 22 -
1
4
1
4
1 p+ 62 +
3
2
12 p- 52610
100 CHAPTER 2 Linear Equations, Inequalities, and Applications
EXERCISES 41– 45
FOR INDIVIDUAL OR GROUP WORK
Work Exercises 41– 45 in order.
41.Solve the linear equation and graph the
solution set on a number line.
42.Solve the linear inequality and graph the
solution set on a number line.
43.Solve the linear inequality and graph the
solution set on a number line.
44.Graph all the solution sets of the equation and inequalities in Exercises 43 – 45on
the same number line. What set do you obtain?
45.Based on the results of Exercises 41 – 43, complete the following, using a
conjecture (educated guess): The solution set of is ,
and the solution set of is. Therefore the solution
set of - 31 x+ 2273 x+ 12 is.
- 31 x+ 2263 x+ 12 1 - 3, q 2
- 31 x+ 22 = 3 x+ 12 5 - 36
51 x+ 32 - 21 x- 42621 x+ 72 ,
51 x+ 32 - 21 x- 42721 x+ 72 ,
51 x+ 32 - 21 x- 42 = 21 x+ 72 ,
RELATING CONCEPTS
46.Concept Check Which is the graph of?
A. B.
C. D.
–2 0 –2 0
–2 0 –2^0
Solve each inequality. Give the solution set in both interval and graph form. See Examples 6
and 7.
Give, in interval notation, the unknown numbers in each description.
59.Six times a number is between and 12.
60.Half a number is between and 2.
61.When 1 is added to twice a number, the result is greater than or equal to 7.
62.If 8 is subtracted from a number, then the result is at least 5.
63.One third of a number is added to 6, giving a result of at least 3.
64.Three times a number, minus 5, is no more than 7.
- 3
- 12
4 ...- 9 x+ 568 4 ...- 2 x+ 368
- 3 ...
3 x+ 1
4
- 1 ... ... 3
2 x- 5
6
... 5
- 19 ... 3 x- 5 ... 1 - 1663 x+ 2 6- 10
- 6 ... 2 x+ 4 ... 16 - 1563 x+ 6 6- 12
- 9 ...x+ 5 ... 15 - 4 ...x+ 3 ... 10
- 46 x- 566 - 16 x+ 168
