Algebra Demystified 2nd Ed

Chapter 9 linear inequaliTieS 341

2. 523 9
   5

≤≤F and FC=+ 32.

5 9

5

32 23

32 32 32

27 9

5

9

5

9

27

1

5

9

9

5

≤+≤

---

-≤ ≤-

⋅- ≤⋅ ≤

C 

C

C^55

9

9

1

15 5

⋅-

-≤≤-C

3. Let x represent the saleswoman’s annual sales. Let s = 15, 000 + 0.10x rep-
   resent her annual salary. She wants 40 000,,≤+15 000^01 .,^06 x≤^0000.

15,000

40 000 15 000 01060000

15 000

,,.,

,

≤+≤

--

x

• ≤≤

15 000

25 000 01045000

25

,

,. ,

,

x

0000

010

010

010

45 000

010

250 000 450 000

.

.

.

,

.

,,

≤≤

≤≤

x

x

She needs to have her annual sales range from $250,000 to $450,000
in order to maintain her annual salary between $40,000 and
$60,000.

4. Let x represent the number of kilowatt-hours the Smiths use per month.
   Then c = 20 + 0.12x represents their monthly electric bill.

80 20 012 110

20 20 20

≤+ ≤

-- -

. x

660 01290

60

012

012

012

90

012

500 750

≤≤

≤≤

≤≤

.

.

.

..

x

x

x

The Smiths would need to keep their monthly usage between 500 and
750 kilowatt-hours to keep their monthly bills in the $80 to $110
range.