home *** CD-ROM | disk | FTP | other *** search
/ Interactive Algebra & Tri…f Guided Study Companion / Interactive Algebra and Trigonometry - A Self-Guided Study Companion.iso / tutor / chap_1 / 1-7-1.tut < prev    next >
Unknown  |  1996-07-12  |  3.7 KB

open in: MacOS 8.1     |     Win98     |     DOS

view JSON data     |     view as text


This file was not able to be converted.
This format is not currently supported by dexvert.

ConfidenceProgramDetectionMatch TypeSupport
1% dexvert Eclipse Tutorial (other/eclipseTutorial) ext Unsupported
1% dexvert JuggleKrazy Tutorial (other/juggleKrazyTutorial) ext Unsupported
100% file data default
100% gt2 Kopftext: 'TUTOR 06A' default (weak)



hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | 41 0e 00 00 85 00 00 00 |TUTOR 06|A.......|
|00000010| 53 65 63 74 69 6f 6e 20 | 31 2e 37 20 20 4c 69 6e |Section |1.7 Lin|
|00000020| 65 61 72 20 49 6e 65 71 | 75 61 6c 69 74 69 65 73 |ear Ineq|ualities|
|00000030| 0d 0b 00 46 6f 72 20 6d | 6f 72 65 20 70 72 61 63 |...For m|ore prac|
|00000040| 74 69 63 65 3a 0d 0a 00 | 0d 0a 00 20 20 20 20 20 |tice:...|... |
|00000050| 10 31 2d 37 2d 33 0e 78 | 31 2d 37 0e 45 78 65 72 |.1-7-3.x|1-7.Exer|
|00000060| 63 69 73 65 73 0f 0d 0a | 00 20 20 20 20 20 10 31 |cises...|. .1|
|00000070| 2d 37 2d 32 0e 65 31 2d | 37 0e 47 75 69 64 65 64 |-7-2.e1-|7.Guided|
|00000080| 20 45 78 65 72 63 69 73 | 65 73 0f 0d 0a 00 0d 0a | Exercis|es......|
|00000090| 00 54 6f 70 69 63 73 20 | 66 6f 72 20 65 78 70 6c |.Topics |for expl|
|000000a0| 6f 72 61 74 69 6f 6e 3a | 0d 0a 00 0d 0a 00 20 20 |oration:|...... |
|000000b0| 20 20 20 0e 73 31 2d 37 | 2d 31 0e 54 68 65 20 54 | .s1-7|-1.The T|
|000000c0| 65 72 6d 69 6e 6f 6c 6f | 67 79 20 6f 66 20 49 6e |erminolo|gy of In|
|000000d0| 65 71 75 61 6c 69 74 69 | 65 73 0f 0d 0a 00 20 20 |equaliti|es.... |
|000000e0| 20 20 20 0e 73 31 2d 37 | 2d 32 0e 50 72 6f 70 65 | .s1-7|-2.Prope|
|000000f0| 72 74 69 65 73 20 6f 66 | 20 49 6e 65 71 75 61 6c |rties of| Inequal|
|00000100| 69 74 69 65 73 0f 0d 0a | 00 20 20 20 20 20 0e 73 |ities...|. .s|
|00000110| 31 2d 37 2d 33 0e 53 6f | 6c 76 69 6e 67 20 61 20 |1-7-3.So|lving a |
|00000120| 4c 69 6e 65 61 72 20 49 | 6e 65 71 75 61 6c 69 74 |Linear I|nequalit|
|00000130| 79 0f 0d 0a 00 20 20 20 | 20 20 0e 73 31 2d 37 2d |y.... | .s1-7-|
|00000140| 34 0e 53 6f 6c 76 69 6e | 67 20 61 6e 20 41 62 73 |4.Solvin|g an Abs|
|00000150| 6f 6c 75 74 65 20 56 61 | 6c 75 65 20 49 6e 65 71 |olute Va|lue Ineq|
|00000160| 75 61 6c 69 74 79 0f 0d | 0a 00 53 65 63 74 69 6f |uality..|..Sectio|
|00000170| 6e 20 31 2e 37 20 20 4c | 69 6e 65 61 72 20 49 6e |n 1.7 L|inear In|
|00000180| 65 71 75 61 6c 69 74 69 | 65 73 0d 0b 00 49 6e 65 |equaliti|es...Ine|
|00000190| 71 75 61 6c 69 74 69 65 | 73 20 74 68 61 74 20 63 |qualitie|s that c|
|000001a0| 6f 6e 74 61 69 6e 20 6f | 6e 65 20 6f 72 20 6d 6f |ontain o|ne or mo|
|000001b0| 72 65 20 76 61 72 69 61 | 62 6c 65 20 74 65 72 6d |re varia|ble term|
|000001c0| 73 20 61 72 65 20 63 61 | 6c 6c 65 64 20 12 31 61 |s are ca|lled .1a|
|000001d0| 6c 67 65 62 72 61 69 63 | 0d 0a 00 69 6e 65 71 75 |lgebraic|...inequ|
|000001e0| 61 6c 69 74 69 65 73 12 | 30 2e 20 20 53 6f 6d 65 |alities.|0. Some|
|000001f0| 20 65 78 61 6d 70 6c 65 | 73 20 61 72 65 0d 0a 00 | example|s are...|
|00000200| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 11 33 78 20 |... | .3x |
|00000210| 11 31 3e 20 2d 31 2c 20 | 20 20 20 11 33 79 20 11 |.1> -1, | .3y .|
|00000220| 31 3c 20 35 2c 20 20 20 | 20 32 11 33 78 20 11 31 |1< 5, | 2.3x .1|
|00000230| 2d 20 31 20 11 34 3e 20 | 11 31 34 2c 20 20 20 20 |- 1 .4> |.14, |
|00000240| 61 6e 64 20 20 20 20 33 | 11 33 78 20 11 31 2b 20 |and 3|.3x .1+ |
|00000250| 32 20 11 34 3c 20 11 33 | 78 20 11 31 2d 20 31 2e |2 .4< .3|x .1- 1.|
|00000260| 0d 0a 00 0d 0b 00 57 65 | 20 12 31 73 6f 6c 76 65 |......We| .1solve|
|00000270| 20 61 6e 20 69 6e 65 71 | 75 61 6c 69 74 79 12 30 | an ineq|uality.0|
|00000280| 20 69 6e 20 74 68 65 20 | 76 61 72 69 61 62 6c 65 | in the |variable|
|00000290| 20 11 33 78 20 11 31 62 | 79 20 66 69 6e 64 69 6e | .3x .1b|y findin|
|000002a0| 67 20 61 6c 6c 20 76 61 | 6c 75 65 73 20 6f 66 20 |g all va|lues of |
|000002b0| 11 33 78 20 11 31 66 6f | 72 20 77 68 69 63 68 0d |.3x .1fo|r which.|
|000002c0| 0a 00 74 68 65 20 69 6e | 65 71 75 61 6c 69 74 79 |..the in|equality|
|000002d0| 20 69 73 20 74 72 75 65 | 2e 20 20 53 75 63 68 20 | is true|. Such |
|000002e0| 76 61 6c 75 65 73 20 61 | 72 65 20 63 61 6c 6c 65 |values a|re calle|
|000002f0| 64 20 12 31 73 6f 6c 75 | 74 69 6f 6e 73 12 30 2c |d .1solu|tions.0,|
|00000300| 20 61 6e 64 20 77 65 20 | 73 61 79 20 74 68 61 74 | and we |say that|
|00000310| 20 74 68 65 0d 0a 00 73 | 6f 6c 75 74 69 6f 6e 73 | the...s|olutions|
|00000320| 20 12 31 73 61 74 69 73 | 66 79 12 30 20 74 68 65 | .1satis|fy.0 the|
|00000330| 20 69 6e 65 71 75 61 6c | 69 74 79 2e 20 20 54 68 | inequal|ity. Th|
|00000340| 65 20 73 65 74 20 6f 66 | 20 61 6c 6c 20 72 65 61 |e set of| all rea|
|00000350| 6c 20 6e 75 6d 62 65 72 | 73 20 74 68 61 74 20 61 |l number|s that a|
|00000360| 72 65 0d 0a 00 73 6f 6c | 75 74 69 6f 6e 73 20 6f |re...sol|utions o|
|00000370| 66 20 74 68 65 20 69 6e | 65 71 75 61 6c 69 74 79 |f the in|equality|
|00000380| 20 69 73 20 63 61 6c 6c | 65 64 20 74 68 65 20 12 | is call|ed the .|
|00000390| 31 73 6f 6c 75 74 69 6f | 6e 20 73 65 74 12 30 20 |1solutio|n set.0 |
|000003a0| 6f 66 20 74 68 65 20 69 | 6e 65 71 75 61 6c 69 74 |of the i|nequalit|
|000003b0| 79 2e 0d 0a 00 0d 0b 00 | 54 68 65 20 73 65 74 20 |y.......|The set |
|000003c0| 6f 66 20 61 6c 6c 20 70 | 6f 69 6e 74 73 20 6f 6e |of all p|oints on|
|000003d0| 20 74 68 65 20 72 65 61 | 6c 20 6e 75 6d 62 65 72 | the rea|l number|
|000003e0| 20 6c 69 6e 65 20 74 68 | 61 74 20 72 65 70 72 65 | line th|at repre|
|000003f0| 73 65 6e 74 73 20 74 68 | 65 20 73 6f 6c 75 74 69 |sents th|e soluti|
|00000400| 6f 6e 20 73 65 74 0d 0a | 00 69 73 20 63 61 6c 6c |on set..|.is call|
|00000410| 65 64 20 74 68 65 20 12 | 31 67 72 61 70 68 12 30 |ed the .|1graph.0|
|00000420| 20 6f 66 20 74 68 65 20 | 69 6e 65 71 75 61 6c 69 | of the |inequali|
|00000430| 74 79 2e 20 20 54 68 65 | 20 67 72 61 70 68 73 20 |ty. The| graphs |
|00000440| 6f 66 20 6d 61 6e 79 20 | 69 6e 65 71 75 61 6c 69 |of many |inequali|
|00000450| 74 69 65 73 20 61 72 65 | 0d 0a 00 69 6e 74 65 72 |ties are|...inter|
|00000460| 76 61 6c 73 20 6f 6e 20 | 74 68 65 20 72 65 61 6c |vals on |the real|
|00000470| 20 6e 75 6d 62 65 72 20 | 6c 69 6e 65 2e 0d 0a 00 | number |line....|
|00000480| 53 65 63 74 69 6f 6e 20 | 31 2e 37 20 20 4c 69 6e |Section |1.7 Lin|
|00000490| 65 61 72 20 49 6e 65 71 | 75 61 6c 69 74 69 65 73 |ear Ineq|ualities|
|000004a0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|000004b0| 20 20 20 20 20 20 20 20 | 20 20 12 31 50 72 6f 70 | | .1Prop|
|000004c0| 65 72 74 69 65 73 20 6f | 66 20 49 6e 65 71 75 61 |erties o|f Inequa|
|000004d0| 6c 69 74 69 65 73 12 30 | 0d 0a 00 4c 65 74 20 11 |lities.0|...Let .|
|000004e0| 33 61 11 31 2c 20 11 33 | 62 11 31 2c 20 11 33 63 |3a.1, .3|b.1, .3c|
|000004f0| 11 31 2c 20 61 6e 64 20 | 11 33 64 20 11 31 62 65 |.1, and |.3d .1be|
|00000500| 20 72 65 61 6c 20 6e 75 | 6d 62 65 72 73 2e 20 20 | real nu|mbers. |
|00000510| 54 68 65 6e 20 74 68 65 | 20 66 6f 6c 6c 6f 77 69 |Then the| followi|
|00000520| 6e 67 20 70 72 6f 70 65 | 72 74 69 65 73 20 61 72 |ng prope|rties ar|
|00000530| 65 20 74 72 75 65 2e 0d | 0a 00 0d 0b 00 31 2e 20 |e true..|.....1. |
|00000540| 12 31 54 72 61 6e 73 69 | 74 69 76 65 20 50 72 6f |.1Transi|tive Pro|
|00000550| 70 65 72 74 79 12 30 0d | 0a 00 0d 0b 00 20 20 20 |perty.0.|..... |
|00000560| 20 20 20 20 20 20 20 20 | 49 66 20 11 33 61 20 11 | |If .3a .|
|00000570| 31 3c 20 11 33 62 20 11 | 31 61 6e 64 20 11 33 62 |1< .3b .|1and .3b|
|00000580| 20 11 31 3c 20 11 33 63 | 11 31 2c 20 74 68 65 6e | .1< .3c|.1, then|
|00000590| 20 11 33 61 20 11 31 3c | 20 11 33 63 11 31 2e 0d | .3a .1<| .3c.1..|
|000005a0| 0a 00 0d 0b 00 32 2e 20 | 12 31 41 64 64 69 74 69 |.....2. |.1Additi|
|000005b0| 6f 6e 20 6f 66 20 49 6e | 65 71 75 61 6c 69 74 69 |on of In|equaliti|
|000005c0| 65 73 12 30 0d 0a 00 0d | 0b 00 20 20 20 20 20 20 |es.0....|.. |
|000005d0| 20 20 20 20 20 49 66 20 | 11 33 61 20 11 31 3c 20 | If |.3a .1< |
|000005e0| 11 33 62 20 11 31 61 6e | 64 20 11 33 63 20 11 31 |.3b .1an|d .3c .1|
|000005f0| 3c 20 11 33 64 11 31 2c | 20 74 68 65 6e 20 11 33 |< .3d.1,| then .3|
|00000600| 61 20 11 31 2b 20 11 33 | 63 20 11 31 3c 20 11 33 |a .1+ .3|c .1< .3|
|00000610| 62 20 11 31 2b 20 11 33 | 64 11 31 2e 0d 0a 00 0d |b .1+ .3|d.1.....|
|00000620| 0b 00 33 2e 20 12 31 41 | 64 64 69 74 69 6f 6e 20 |..3. .1A|ddition |
|00000630| 6f 66 20 61 20 43 6f 6e | 73 74 61 6e 74 12 30 0d |of a Con|stant.0.|
|00000640| 0a 00 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |..... | |
|00000650| 49 66 20 11 33 61 20 11 | 31 3c 20 11 33 62 11 31 |If .3a .|1< .3b.1|
|00000660| 2c 20 74 68 65 6e 20 11 | 33 61 20 11 31 2b 20 11 |, then .|3a .1+ .|
|00000670| 33 63 20 11 31 3c 20 11 | 33 62 20 11 31 2b 20 11 |3c .1< .|3b .1+ .|
|00000680| 33 63 11 31 2e 0d 0a 00 | 0d 0b 00 34 2e 20 12 31 |3c.1....|...4. .1|
|00000690| 4d 75 6c 74 69 70 6c 69 | 63 61 74 69 6f 6e 20 62 |Multipli|cation b|
|000006a0| 79 20 61 20 43 6f 6e 73 | 74 61 6e 74 12 30 0d 0a |y a Cons|tant.0..|
|000006b0| 00 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 28 |.... | (|
|000006c0| 69 29 20 46 6f 72 20 11 | 33 63 20 11 31 3e 20 30 |i) For .|3c .1> 0|
|000006d0| 2c 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |,...... | |
|000006e0| 20 20 20 20 20 20 20 69 | 66 20 11 33 61 20 11 31 | i|f .3a .1|
|000006f0| 3c 20 11 33 62 11 31 2c | 20 74 68 65 6e 20 11 33 |< .3b.1,| then .3|
|00000700| 61 63 20 11 31 3c 20 11 | 33 62 63 11 31 2e 0d 0a |ac .1< .|3bc.1...|
|00000710| 00 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 28 69 |.... | (i|
|00000720| 69 29 20 46 6f 72 20 11 | 33 63 20 11 31 3c 20 30 |i) For .|3c .1< 0|
|00000730| 2c 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |,...... | |
|00000740| 20 20 20 20 20 20 20 69 | 66 20 11 33 61 20 11 31 | i|f .3a .1|
|00000750| 3c 20 11 33 62 11 31 2c | 20 74 68 65 6e 20 11 33 |< .3b.1,| then .3|
|00000760| 61 63 20 11 31 3e 20 11 | 33 62 63 11 31 2e 0d 0a |ac .1> .|3bc.1...|
|00000770| 00 53 65 63 74 69 6f 6e | 20 31 2e 37 20 20 4c 69 |.Section| 1.7 Li|
|00000780| 6e 65 61 72 20 49 6e 65 | 71 75 61 6c 69 74 69 65 |near Ine|qualitie|
|00000790| 73 0d 0b 00 54 68 65 20 | 69 6e 65 71 75 61 6c 69 |s...The |inequali|
|000007a0| 74 69 65 73 0d 0a 00 0d | 0b 00 20 20 20 20 20 20 |ties....|.. |
|000007b0| 32 11 33 78 20 11 31 3c | 20 35 2c 20 20 20 20 11 |2.3x .1<| 5, .|
|000007c0| 33 78 20 11 31 2b 20 34 | 20 3e 20 2d 31 2c 20 20 |3x .1+ 4| > -1, |
|000007d0| 20 20 32 20 2d 20 33 11 | 33 78 20 11 34 3c 20 11 | 2 - 3.|3x .4< .|
|000007e0| 31 35 2c 20 20 20 20 61 | 6e 64 20 20 20 20 37 11 |15, a|nd 7.|
|000007f0| 33 78 20 11 34 3e 20 11 | 31 32 11 33 78 20 11 31 |3x .4> .|12.3x .1|
|00000800| 2d 20 33 0d 0a 00 0d 0b | 00 61 72 65 20 65 61 63 |- 3.....|.are eac|
|00000810| 68 20 12 31 6c 69 6e 65 | 61 72 20 69 6e 65 71 75 |h .1line|ar inequ|
|00000820| 61 6c 69 74 69 65 73 12 | 30 20 69 6e 20 74 68 65 |alities.|0 in the|
|00000830| 20 76 61 72 69 61 62 6c | 65 20 11 33 78 20 11 31 | variabl|e .3x .1|
|00000840| 62 65 63 61 75 73 65 20 | 74 68 65 20 28 69 6d 70 |because |the (imp|
|00000850| 6c 69 65 64 29 20 65 78 | 70 6f 6e 65 6e 74 0d 0a |lied) ex|ponent..|
|00000860| 00 6f 66 20 11 33 78 20 | 11 31 69 6e 20 65 61 63 |.of .3x |.1in eac|
|00000870| 68 20 69 6e 65 71 75 61 | 6c 69 74 79 20 69 73 20 |h inequa|lity is |
|00000880| 31 2e 20 20 54 6f 20 12 | 31 73 6f 6c 76 65 20 61 |1. To .|1solve a|
|00000890| 20 6c 69 6e 65 61 72 20 | 69 6e 65 71 75 61 6c 69 | linear |inequali|
|000008a0| 74 79 12 30 20 77 65 20 | 77 72 69 74 65 20 61 20 |ty.0 we |write a |
|000008b0| 0d 0a 00 73 65 71 75 65 | 6e 63 65 20 6f 66 20 12 |...seque|nce of .|
|000008c0| 31 65 71 75 69 76 61 6c | 65 6e 74 12 30 20 69 6e |1equival|ent.0 in|
|000008d0| 65 71 75 61 6c 69 74 69 | 65 73 20 75 73 69 6e 67 |equaliti|es using|
|000008e0| 20 74 68 65 20 70 72 6f | 70 65 72 74 69 65 73 20 | the pro|perties |
|000008f0| 64 65 73 63 72 69 62 65 | 64 20 6f 6e 0d 0a 00 70 |describe|d on...p|
|00000900| 61 67 65 20 31 35 34 20 | 6f 66 20 79 6f 75 72 20 |age 154 |of your |
|00000910| 74 65 78 74 2e 0d 0a 00 | 54 68 65 20 69 6e 65 71 |text....|The ineq|
|00000920| 75 61 6c 69 74 69 65 73 | 0d 0a 00 0d 0b 00 20 20 |ualities|...... |
|00000930| 20 20 20 20 20 20 20 20 | 20 20 2d 32 20 11 34 3c | | -2 .4<|
|00000940| 20 11 31 32 11 33 78 20 | 11 31 2b 20 35 20 3c 20 | .12.3x |.1+ 5 < |
|00000950| 38 20 20 20 20 20 20 20 | 20 61 6e 64 20 20 20 20 |8 | and |
|00000960| 20 20 20 20 34 20 3c 20 | 33 20 2d 20 11 33 78 20 | 4 < |3 - .3x |
|00000970| 11 34 3c 20 11 31 38 0d | 0a 00 0d 0b 00 61 72 65 |.4< .18.|.....are|
|00000980| 20 63 61 6c 6c 65 64 20 | 12 31 64 6f 75 62 6c 65 | called |.1double|
|00000990| 20 69 6e 65 71 75 61 6c | 69 74 69 65 73 12 30 20 | inequal|ities.0 |
|000009a0| 62 65 63 61 75 73 65 20 | 74 68 65 79 20 61 63 74 |because |they act|
|000009b0| 75 61 6c 6c 79 20 63 6f | 6e 74 61 69 6e 20 74 77 |ually co|ntain tw|
|000009c0| 6f 20 69 6e 65 71 75 61 | 6c 69 74 69 65 73 2e 0d |o inequa|lities..|
|000009d0| 0a 00 0d 0b 00 20 20 2d | 32 20 11 34 3c 20 11 31 |..... -|2 .4< .1|
|000009e0| 32 11 33 78 20 11 31 2b | 20 35 20 20 20 26 20 20 |2.3x .1+| 5 & |
|000009f0| 20 32 11 33 78 20 11 31 | 2b 20 35 20 3c 20 38 20 | 2.3x .1|+ 5 < 8 |
|00000a00| 20 20 20 20 61 6e 64 20 | 20 20 20 20 34 20 3c 20 | and | 4 < |
|00000a10| 33 20 2d 20 11 33 78 20 | 20 20 11 31 26 20 20 20 |3 - .3x | .1& |
|00000a20| 33 20 2d 20 11 33 78 20 | 11 34 3c 20 11 31 38 0d |3 - .3x |.4< .18.|
|00000a30| 0a 00 0d 0b 00 54 6f 20 | 12 31 73 6f 6c 76 65 20 |.....To |.1solve |
|00000a40| 61 20 64 6f 75 62 6c 65 | 20 69 6e 65 71 75 61 6c |a double| inequal|
|00000a50| 69 74 79 12 30 20 77 65 | 20 75 73 65 20 74 68 65 |ity.0 we| use the|
|00000a60| 20 73 61 6d 65 20 74 65 | 63 68 6e 69 71 75 65 73 | same te|chniques|
|00000a70| 20 75 73 65 64 20 66 6f | 72 20 61 20 73 69 6e 67 | used fo|r a sing|
|00000a80| 6c 65 0d 0a 00 69 6e 65 | 71 75 61 6c 69 74 79 2e |le...ine|quality.|
|00000a90| 20 20 54 68 65 20 66 6f | 72 6d 20 6f 66 20 61 20 | The fo|rm of a |
|00000aa0| 64 6f 75 62 6c 65 20 69 | 6e 65 71 75 61 6c 69 74 |double i|nequalit|
|00000ab0| 79 20 73 69 6d 70 6c 79 | 20 61 6c 6c 6f 77 73 20 |y simply| allows |
|00000ac0| 75 73 20 74 6f 20 73 6f | 6c 76 65 20 74 77 6f 0d |us to so|lve two.|
|00000ad0| 0a 00 69 6e 65 71 75 61 | 6c 69 74 69 65 73 20 61 |..inequa|lities a|
|00000ae0| 74 20 74 68 65 20 73 61 | 6d 65 20 74 69 6d 65 2e |t the sa|me time.|
|00000af0| 20 20 46 6f 72 20 61 20 | 64 65 6d 6f 6e 73 74 72 | For a |demonstr|
|00000b00| 61 74 69 6f 6e 20 6f 66 | 20 68 6f 77 20 74 68 69 |ation of| how thi|
|00000b10| 73 20 77 6f 72 6b 73 2c | 20 73 65 65 0d 0a 00 45 |s works,| see...E|
|00000b20| 78 61 6d 70 6c 65 20 34 | 20 6f 6e 20 70 61 67 65 |xample 4| on page|
|00000b30| 20 31 35 36 20 6f 66 20 | 79 6f 75 72 20 74 65 78 | 156 of |your tex|
|00000b40| 74 20 6f 72 20 73 74 75 | 64 79 20 47 75 69 64 65 |t or stu|dy Guide|
|00000b50| 64 20 45 78 61 6d 70 6c | 65 20 33 20 69 6e 20 74 |d Exampl|e 3 in t|
|00000b60| 68 69 73 20 73 65 63 74 | 69 6f 6e 2e 0d 0a 00 53 |his sect|ion....S|
|00000b70| 65 63 74 69 6f 6e 20 31 | 2e 37 20 20 4c 69 6e 65 |ection 1|.7 Line|
|00000b80| 61 72 20 49 6e 65 71 75 | 61 6c 69 74 69 65 73 0d |ar Inequ|alities.|
|00000b90| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00000ba0| 20 20 20 20 20 12 31 53 | 6f 6c 76 69 6e 67 20 61 | .1S|olving a|
|00000bb0| 6e 20 41 62 73 6f 6c 75 | 74 65 20 56 61 6c 75 65 |n Absolu|te Value|
|00000bc0| 20 49 6e 65 71 75 61 6c | 69 74 79 12 30 0d 0a 00 | Inequal|ity.0...|
|00000bd0| 0d 0b 00 4c 65 74 20 11 | 33 78 20 11 31 62 65 20 |...Let .|3x .1be |
|00000be0| 61 20 76 61 72 69 61 62 | 6c 65 20 6f 72 20 61 6e |a variab|le or an|
|00000bf0| 20 61 6c 67 65 62 72 61 | 69 63 20 65 78 70 72 65 | algebra|ic expre|
|00000c00| 73 73 69 6f 6e 20 61 6e | 64 20 6c 65 74 20 11 33 |ssion an|d let .3|
|00000c10| 61 20 11 31 62 65 20 61 | 20 72 65 61 6c 20 6e 75 |a .1be a| real nu|
|00000c20| 6d 62 65 72 20 73 75 63 | 68 0d 0a 00 74 68 61 74 |mber suc|h...that|
|00000c30| 20 11 33 61 20 11 34 3e | 20 11 31 30 2e 0d 0a 00 | .3a .4>| .10....|
|00000c40| 0d 0b 00 31 2e 20 20 54 | 68 65 20 73 6f 6c 75 74 |...1. T|he solut|
|00000c50| 69 6f 6e 73 20 6f 66 20 | 7c 11 33 78 11 31 7c 20 |ions of ||.3x.1| |
|00000c60| 3c 20 11 33 61 20 11 31 | 61 72 65 20 61 6c 6c 20 |< .3a .1|are all |
|00000c70| 76 61 6c 75 65 73 20 6f | 66 20 11 33 78 20 11 31 |values o|f .3x .1|
|00000c80| 74 68 61 74 20 6c 69 65 | 20 62 65 74 77 65 65 6e |that lie| between|
|00000c90| 20 2d 11 33 61 20 11 31 | 61 6e 64 20 11 33 61 11 | -.3a .1|and .3a.|
|00000ca0| 31 2e 0d 0a 00 20 20 20 | 20 54 68 61 74 20 69 73 |1.... | That is|
|00000cb0| 2c 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |,... | |
|00000cc0| 20 20 20 20 7c 11 33 78 | 11 31 7c 20 3c 20 11 33 | |.3x|.1| < .3|
|00000cd0| 61 20 20 20 20 20 11 31 | 69 66 20 61 6e 64 20 6f |a .1|if and o|
|00000ce0| 6e 6c 79 20 69 66 20 20 | 20 20 20 2d 11 33 61 20 |nly if | -.3a |
|00000cf0| 11 31 3c 20 11 33 78 20 | 11 31 3c 20 11 33 61 11 |.1< .3x |.1< .3a.|
|00000d00| 31 2e 0d 0a 00 0d 0b 00 | 32 2e 20 20 54 68 65 20 |1.......|2. The |
|00000d10| 73 6f 6c 75 74 69 6f 6e | 73 20 6f 66 20 7c 11 33 |solution|s of |.3|
|00000d20| 78 11 31 7c 20 3e 20 11 | 33 61 20 11 31 61 72 65 |x.1| > .|3a .1are|
|00000d30| 20 61 6c 6c 20 76 61 6c | 75 65 73 20 6f 66 20 11 | all val|ues of .|
|00000d40| 33 78 20 11 31 74 68 61 | 74 20 61 72 65 20 6c 65 |3x .1tha|t are le|
|00000d50| 73 73 20 74 68 61 6e 20 | 2d 11 33 61 20 11 31 6f |ss than |-.3a .1o|
|00000d60| 72 0d 0a 00 20 20 20 20 | 67 72 65 61 74 65 72 20 |r... |greater |
|00000d70| 74 68 61 6e 20 11 33 61 | 11 31 2e 20 20 54 68 61 |than .3a|.1. Tha|
|00000d80| 74 20 69 73 2c 0d 0a 00 | 0d 0b 00 20 20 20 20 20 |t is,...|... |
|00000d90| 20 20 20 20 20 20 20 20 | 20 20 20 7c 11 33 78 11 | | |.3x.|
|00000da0| 31 7c 20 3e 20 11 33 61 | 20 20 20 20 20 11 31 69 |1| > .3a| .1i|
|00000db0| 66 20 61 6e 64 20 6f 6e | 6c 79 20 69 66 20 20 20 |f and on|ly if |
|00000dc0| 20 20 11 33 78 20 11 31 | 3c 20 2d 11 33 61 20 20 | .3x .1|< -.3a |
|00000dd0| 11 31 6f 72 20 20 11 33 | 78 20 11 31 3e 20 11 33 |.1or .3|x .1> .3|
|00000de0| 61 11 31 2e 0d 0a 00 0d | 0b 00 54 68 65 73 65 20 |a.1.....|..These |
|00000df0| 74 77 6f 20 72 75 6c 65 | 73 20 61 72 65 20 61 6c |two rule|s are al|
|00000e00| 73 6f 20 76 61 6c 69 64 | 20 69 66 20 3c 20 69 73 |so valid| if < is|
|00000e10| 20 72 65 70 6c 61 63 65 | 64 20 62 79 20 11 34 3c | replace|d by .4<|
|00000e20| 20 11 31 61 6e 64 20 3e | 20 69 73 20 72 65 70 6c | .1and >| is repl|
|00000e30| 61 63 65 64 20 62 79 20 | 11 34 3e 11 31 2e 0d 0a |aced by |.4>.1...|
|00000e40| 00 30 00 00 00 3a 01 00 | 00 4d 20 00 00 10 00 00 |.0...:..|.M .....|
|00000e50| 00 00 00 00 00 73 31 2d | 37 00 8a 01 00 00 f6 02 |.....s1-|7.......|
|00000e60| 00 00 4d 20 00 00 6a 01 | 00 00 00 00 00 00 73 31 |..M ..j.|......s1|
|00000e70| 2d 37 2d 31 00 a0 04 00 | 00 d1 02 00 00 4d 20 00 |-7-1....|.....M .|
|00000e80| 00 80 04 00 00 00 00 00 | 00 73 31 2d 37 2d 32 00 |........|.s1-7-2.|
|00000e90| 91 07 00 00 de 03 00 00 | 4d 20 00 00 71 07 00 00 |........|M ..q...|
|00000ea0| 00 00 00 00 73 31 2d 37 | 2d 33 00 8f 0b 00 00 b2 |....s1-7|-3......|
|00000eb0| 02 00 00 4d 20 00 00 6f | 0b 00 00 00 00 00 00 73 |...M ..o|.......s|
|00000ec0| 31 2d 37 2d 34 00 | |1-7-4. | |
+--------+-------------------------+-------------------------+--------+--------+