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- Destinyyyy

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- Destinyyyy

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

- Destinyyyy

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

- Destinyyyy

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

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## More answers

- linn99123

okay so whats ur answer for number 1?

- Destinyyyy

I posted both of my answers above.

- Destinyyyy

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

- DanJS

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

- dinamix

and i am sure about my answer

- Destinyyyy

Okay

- xapproachesinfinity

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

- Destinyyyy

Where are you getting 189 from???

- DanJS

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

- xapproachesinfinity

36+9/5=189/5

- Destinyyyy

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

- xapproachesinfinity

eh should be 180-9 i added them

- xapproachesinfinity

it is ok well make mistakes

- xapproachesinfinity

we all*

- xapproachesinfinity

but the she got the point

- Destinyyyy

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

- xapproachesinfinity

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

- xapproachesinfinity

you know how this works that's what is important

- xapproachesinfinity

i got the same result you should be good to go

- 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

- xapproachesinfinity

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

- xapproachesinfinity

if you multiply by negative you should change the inequality

- 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.

- dinamix

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

- Destinyyyy

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

- dinamix

yup i was wrong its 189/10 sorry

- dinamix

i forget add 18/2 only sorry

- Destinyyyy

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

- xapproachesinfinity

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

- xapproachesinfinity

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

- xapproachesinfinity

second x>153/10

- dinamix

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

- xapproachesinfinity

actually you made a mistake somewhere for the scond

- dinamix

i fix it now

- xapproachesinfinity

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

- dinamix

this is not - its just Arrow

- Destinyyyy

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

- Destinyyyy

What are you talking about? Its over 5 not 10

- dinamix

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

- xapproachesinfinity

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

- xapproachesinfinity

that what i meant she made a mistake in calculations

- xapproachesinfinity

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

- xapproachesinfinity

you should get that same answer you have by mathway

- xapproachesinfinity

over 10 my bad

- Destinyyyy

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

- Destinyyyy

I dont understand your multiple by -1/2.

- xapproachesinfinity

you need to isolate x right

- xapproachesinfinity

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

- xapproachesinfinity

it is like you do with equation to islote the unknown

- Destinyyyy

...

- Destinyyyy

Still dont understand.

- xapproachesinfinity

how would you solve 2x=4

- Destinyyyy

Divide both sides by 2.

- xapproachesinfinity

so same thing divide the inequality both sides by 2

- xapproachesinfinity

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

- Destinyyyy

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

- xapproachesinfinity

why decimal ? you get -153/5x2

- xapproachesinfinity

i dont see where do you get decimal?

- Destinyyyy

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

- xapproachesinfinity

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

- 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

- xapproachesinfinity

you making this hard on youself

- dinamix

cuz i think this is right answer @xapproachesinfinity

- 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???

- xapproachesinfinity

yes your answer is good @dinamix

- 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 ?

- xapproachesinfinity

heheheh thanks
i thought i made efforts to show you

- Destinyyyy

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

- dinamix

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

- xapproachesinfinity

ok dinamix take over i have to go

- dinamix

@xapproachesinfinity plz i dont know how to explain

- Destinyyyy

Try showing me?

- dinamix

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

- dinamix

@Destinyyyy what i show u

- Destinyyyy

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

- dinamix

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

- dinamix

that what u mean or what

- 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.

- Destinyyyy

The fist sign goes < not >

- Destinyyyy

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

- dinamix

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

- dinamix

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

- 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

- dinamix

@freckles like my steps lol

- freckles

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

- freckles

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

- dinamix

@freckles but why we get same result

- freckles

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

- 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.

- dinamix

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

- Destinyyyy

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

- Destinyyyy

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

- freckles

alright
one more
and then I eat

- Destinyyyy

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

- freckles

\[\frac{x}{4}-\frac{1}{5} \le \frac{x}{5}+1\]

- freckles

is that correct

- Destinyyyy

I got x

- freckles

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

- freckles

assumed*

- dinamix

x<24 i find it

- Destinyyyy

My example had me plus 1/5 to both sides.
So I have x/4

- freckles

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

- 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

- Destinyyyy

x

- dinamix

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

- Destinyyyy

(- infinity sign, 24]

- Destinyyyy

Im a her....

- dinamix

yup @Destinyyyy this the answer hreat now u understand

- dinamix

ok i was joke only

- 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

- dinamix

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

- dinamix

@Destinyyyy and u can will be like that

- Destinyyyy

The example I followed didnt show me like that..
It did
x/4

- dinamix

pen*

- 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

- freckles

np i will eat now

- dinamix

u make mistake in line 4

- Destinyyyy

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

- dinamix

\[\frac{ 5x -4x}{ 20 }\]

- dinamix

=\[\frac{ x }{ 4}-\frac{ x }{ 5 }\]

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