## Destinyyyy one year ago Need two problems checked...

1. Destinyyyy

Solve the absolute value inequality. 36< {-2x+18/5} +9/5 {} absolute value

2. Destinyyyy

180/5 <{-2x+ 18/5} -2x+18/5> 180/5 -2x+ 18/5< -180/5

3. Destinyyyy

I got-- x> -81/5 x< 99/5

4. linn99123

okay so whats ur answer for number 1?

5. Destinyyyy

I posted both of my answers above.

6. Destinyyyy

Im not sure what you mean by number one. I only posted one question.

7. DanJS

looks like you know the way to solve them, not sure about the numbers

8. dinamix

9. Destinyyyy

Okay

10. xapproachesinfinity

$$|-2x+18/5|+9/5>36$$ $$|-2x+18/5|>189/5 \leftarrow \text{one correction here}$$

11. Destinyyyy

Where are you getting 189 from???

12. DanJS

36 - (9/5) = 171/5 for the first thing

13. xapproachesinfinity

36+9/5=189/5

14. Destinyyyy

Omg... 36 *5= 180 .. I forgot to minus the 9 -.-

15. xapproachesinfinity

eh should be 180-9 i added them

16. xapproachesinfinity

it is ok well make mistakes

17. xapproachesinfinity

we all*

18. xapproachesinfinity

but the she got the point

19. Destinyyyy

Now I have -2x> 153/5 -2x < -153/5

20. xapproachesinfinity

yah yo got the point of this just made some few error just recheck for certainty

21. xapproachesinfinity

you know how this works that's what is important

22. xapproachesinfinity

i got the same result you should be good to go

23. Destinyyyy

Okay. But now im stuck.. -2 cant be divided into these. And my last problem like this just divided the top number by -2

24. xapproachesinfinity

multiply by -1/2 and switch the sign > to < and < to >

25. xapproachesinfinity

if you multiply by negative you should change the inequality

26. Destinyyyy

Uh? I know what the final answer is because I looked it up on mathway... But dont get how I go from what I have to it.

27. dinamix

@Destinyyyy u have find it 171/10< x<-153/10 i didnt focus first time

28. Destinyyyy

The answer is (- infinity sign, -153/10) u (189/10 , infinity sign)

29. dinamix

yup i was wrong its 189/10 sorry

30. dinamix

i forget add 18/2 only sorry

31. Destinyyyy

How do I get from -2x> 153/5 and -2x< -153/5 to the final answer

32. xapproachesinfinity

i told you to multiply by -1/2 both sides

33. xapproachesinfinity

first one x<-153/10 see the inequality changed

34. xapproachesinfinity

second x>153/10

35. dinamix

not that u have -2x>153/5 ------ 2x<-153/5 -----x<-153/10 @Destinyyyy

36. xapproachesinfinity

actually you made a mistake somewhere for the scond

37. dinamix

i fix it now

38. xapproachesinfinity

it should not be -2x<-153/5

39. dinamix

this is not - its just Arrow

40. Destinyyyy

Then Id have to change the denominators to 10... 306/10 5/10 .. Do I minus, divide, multiple?

41. Destinyyyy

What are you talking about? Its over 5 not 10

42. dinamix

not that u have (-2x>153/5) ------ (2x<-153/5) -----(x<-153/10 ) @xapproachesinfinity this what i mean

43. xapproachesinfinity

the second should have been -2x<-189/5 then x>189/10

44. xapproachesinfinity

that what i meant she made a mistake in calculations

45. xapproachesinfinity

after that just read what x<-153/10 and x>189/10 mean in interval nottion

46. xapproachesinfinity

you should get that same answer you have by mathway

47. xapproachesinfinity

48. Destinyyyy

OMG. Seriously. Im an still at -2x> 153/5 and -2x< -153/5

49. Destinyyyy

I dont understand your multiple by -1/2.

50. xapproachesinfinity

you need to isolate x right

51. xapproachesinfinity

so we multiply by a minus sign which switches the inequality then we multiply by 1/2 to get rid of 2

52. xapproachesinfinity

it is like you do with equation to islote the unknown

53. Destinyyyy

...

54. Destinyyyy

Still dont understand.

55. xapproachesinfinity

how would you solve 2x=4

56. Destinyyyy

Divide both sides by 2.

57. xapproachesinfinity

so same thing divide the inequality both sides by 2

58. xapproachesinfinity

that is the same as multiplying out by 1/2 hahaha

59. Destinyyyy

Okay. Like I said before its not possible. It gives a decimal.... K? So then Id have to change both denominators to 10.

60. xapproachesinfinity

why decimal ? you get -153/5x2

61. xapproachesinfinity

i dont see where do you get decimal?

62. Destinyyyy

What are you talking about? 153 divided by -2= -76.5

63. xapproachesinfinity

why you need to divide? leave it 153/5x2=153/10

64. dinamix

$|-2x+\frac{ 18 }{ 2 }|>\frac{ 171 }{ 5 }$ $\frac{ -171}{ 5 }>-2x+\frac{ 18 }{ 2 }>\frac{ 171 }{ 5}$ $\frac{ -171-18 }{ 5 }>-2x>\frac{ 171-18 }{ 5}$ $\frac{ -189 }{ 5}>-2x>\frac{ 153 }{ 5 }$ $-\frac{ 153 }{ 10 }>x>\frac{ 189 }{ 10 }$ @xapproachesinfinity could u check my mistake @Destinyyyy this is real solution

65. xapproachesinfinity

you making this hard on youself

66. dinamix

cuz i think this is right answer @xapproachesinfinity

67. Destinyyyy

No im not. You are making this impossible to understand. Ive waited 2 hours for help and now Im just confused. Normally you just divide it. And instead im suppose to multiple it. But all you did was change the denominator. Why???

68. xapproachesinfinity

69. Destinyyyy

You said to multiply by 1/2 so I asked about changing both denominator to 10. And both times you did not respond. So im just suppose to do 5*2= 10 ?

70. xapproachesinfinity

heheheh thanks i thought i made efforts to show you

71. Destinyyyy

I understand the first one. Now what about the other one.

72. dinamix

@xapproachesinfinity ty @Destinyyyy what u didnt understand we can help u

73. xapproachesinfinity

ok dinamix take over i have to go

74. dinamix

@xapproachesinfinity plz i dont know how to explain

75. Destinyyyy

Try showing me?

76. dinamix

its hard to expalin idea for me @xapproachesinfinity this problem of me

77. dinamix

@Destinyyyy what i show u

78. Destinyyyy

Can you just show me how you went from -2x< -153/5 to 189/10

79. dinamix

-2x>153/5 to x<-153/10 right ?

80. dinamix

that what u mean or what

81. Destinyyyy

If I go off from what both of you said before by just multiplying by -1/2 then Ill just get 153/10 which is not the correct answer. Which also makes me think how you said to solve the first one is not the correct way to solve it.

82. Destinyyyy

The fist sign goes < not >

83. Destinyyyy

-2x< -153/5 to 189/10

84. dinamix

$-2x+\frac{ 18 }{ 5} > 171/5$ and $-(-2x+\frac{ 18 }{ 5 })>171/5$$\frac{ -171 }{ 5 } >-2x+\frac{ 18 }{ 5 }>\frac{ 171 }{ 5}$

85. dinamix

@Destinyyyy its 2 equation i make it only one did u understand now

86. freckles

36< |-2x+18/5| +9/5 Just because I like to write the absolute value expression first then the inequality thingy.. $|-2x+\frac{18}{5}|+\frac{9}{5}>36 \\ \text{ so you subtracted } \frac{9}{5} \text{ on both sides } \\ |-2x+\frac{18}{5}|>36-\frac{9}{5} \\ |-2x+\frac{18}{5}|> \frac{180-9}{5} \\ |-2x+\frac{18}{5}| >\frac{171}{5} \\ \text{ now since this is a greater than we have a union } \\ \text{ that is we have } -2x+\frac{18}{5}<-\frac{171}{5} \text{ or } -2x+\frac{18}{5}>\frac{171}{5} \\ \text{ for both inequalities subtract }\frac{18}{5} \text{ on both sides } \\ -2x<\frac{-171}{5}-\frac{18}{5} \text{ or } -2x> \frac{171}{5}-\frac{18}{5} \\ \text{ simplifying right hand sides } \\ -2x <\frac{-189}{5} \text{ or } -2x >\frac{153}{5} \\ \text{ now you can say divide both sides by -2 } \\ \text{ or equivalently say multiply both sides by } \frac{-1}{2} \\ \text{ this is the same meaning just different saying }$ $\frac{-1}{2} \cdot (-2x)>\frac{-1}{2}(\frac{-189}{5}) \text{ change direction of inequality symbol } \\ \text{ since I multiplied both sides by a negative } \\ x>\frac{189}{10} \\ \text{ now the other inequality } \\ \frac{-1}{2}(-2x)<\frac{-1}{2}(\frac{153}{5}) \\ x<\frac{-153}{10}$ so put the two pieces together and put or between them

87. dinamix

@freckles like my steps lol

88. freckles

$x<\frac{-153}{10} \text{ or } x>\frac{189}{10}$

89. freckles

your solution seems to suggest -171 is greater than 171 since it says -171/5>171/5 @dinamix

90. dinamix

@freckles but why we get same result

91. freckles

no I didn't get -171>171 because this is not true

92. Destinyyyy

Omg thank you @freckles I completely understood everything you said. And I saw where I messed up. I did write down the - for -171/5 so when I minus-ed the 18 I had the wrong answer. Now I have the correct one and understand how to solve the ending.

93. dinamix

but @freckles look the last i get -153/10 >x or x>189/10 look

94. Destinyyyy

And all that turns into (- infinity sign, -153/10) u (189/10, infinity sign)

95. Destinyyyy

@freckles Can you check one more? I know that my answer is wrong, but im not sure how it is.

96. freckles

alright one more and then I eat

97. Destinyyyy

Okay... Use interval notation to express the solution set and graph the solution set on a number line. x/4 - 1/5 </ x/5 +1

98. freckles

$\frac{x}{4}-\frac{1}{5} \le \frac{x}{5}+1$

99. freckles

is that correct

100. Destinyyyy

I got x</ 2 (- infinity sign, 2] But it says im wrong Yes thats correct

101. freckles

so I retriceumed you subtracted x/5 on both sides and added 1/5 on both sides?

102. freckles

assumed*

103. dinamix

x<24 i find it

104. Destinyyyy

My example had me plus 1/5 to both sides. So I have x/4 </ x/5 +1 +1/5 Then add the +1 and 1/5 together x/4 </ x/5 +6/5

105. freckles

@Destinyyyy if you don't like the fractions before moving anything you can multiply both sides by 4*5=20

106. freckles

$(20)(\frac{x}{4}-\frac{1}{5} ) \le 20(\frac{x}{5}+1) \\ \frac{20}{4}x-\frac{20}{5} \le \frac{20}{5}x+20 \\ 5x-4 \le 4x+20$ this might make it easier for you

107. Destinyyyy

x</ 24

108. dinamix

@freckles ty for help her or him anyway , i know the answer but i dont how eplain idea this my problem

109. Destinyyyy

(- infinity sign, 24]

110. Destinyyyy

Im a her....

111. dinamix

yup @Destinyyyy this the answer hreat now u understand

112. dinamix

ok i was joke only

113. freckles

yep now if you didn't do the whole canceling fraction thing... $\frac{x}{4}-\frac{1}{5} \le \frac{x}{5}+1 \\ \text{ subtract } \frac{x}{5} \text{ on both sides } \\ \frac{x}{4} -\frac{x}{5}-\frac{1}{5} \le 1 \\ \text{ now add } \frac{1}{5} \text{ on both sides } \\ \frac{x}{4} -\frac{x}{5} \le 1+\frac{1}{5} \\ \\ \text{ find common denominators } \\ \frac{5x-4x}{20} \le \frac{5+1}{5} \\ \frac{1x}{20} \le \frac{6}{5} \\ \frac{x}{20} \le \frac{6}{5} \\ \text{ multiply both side by } 20 \\ x \le \frac{6(20)}{5} \\ x \le 6 \cdot \frac{20}{5} \\ x \le 6 (4) \\ x \le 24$ just so you know how it looks without removing fractions first

114. dinamix

@Destinyyyy i find it without use pain last question ;D

115. dinamix

@Destinyyyy and u can will be like that

116. Destinyyyy

The example I followed didnt show me like that.. It did x/4 </ x/5 +1 +1/5 x/4 </ x+5 +6/5 x/4 -x/5 </ 6/5 4x-x/5 </ 6/5 4x-x </ 6 3x</ 6 x</2

117. dinamix

pen*

118. Destinyyyy

So I would have gotten the right answer if it had told me to do over 20 instead of over 5.. Which I thought was weird. Thank you for helping! @freckles

119. freckles

np i will eat now

120. dinamix

u make mistake in line 4

121. Destinyyyy

Yeah I know that. But that's what the example said to do so I did.

122. dinamix

$\frac{ 5x -4x}{ 20 }$

123. dinamix

=$\frac{ x }{ 4}-\frac{ x }{ 5 }$