Question

absolute value problem help please

Answer 1

oh goodie

Answer 2

\[4\left| 4-5x \right| = 6x+4\]

Answer 3

lol

Answer 4

oh this is going to be much more of a drag

Answer 5

x=6/13,10/7

Answer 6

that was wrong, sorry

Answer 7

it's okay

Answer 8

@satellite73 Can the absolute value brackets act like parentheses, and you can use the distributive property on them or no?

Answer 9

\[4\left| 4-5x \right| = 6x+4\] divide by \(4\) and start with
\[|5x-4|=\frac{3}{2}x+1\] is more like it

Answer 10

or you can do as @ShadowLegendX suggests and distribute the 4 and start with
\[|16-20x|=6x+4\]

Answer 11

but then you have to be careful and work in cases

\[|16-20x|=|20x-16|=20x-16\] if \(20x-16\geq 0\) i.e. if \(x\geq \frac{4}{5}\) and it is
\[16-20x\]if \(x<\frac{4}{5}\)

Answer 12

wait above you wrote 5x-4 did you mean 4-5x?

Answer 13

good question!

Answer 14

and the answer is, it makes no difference. it is always the case that \(|a-b|=|b-a|\) so
\[|5x-4|=|4-5x|\]

Answer 15

oh yea because of the absolute value

Answer 16

so lets solve
\[20x-16=6x+4\]

Answer 17

this is case 1 right?

Answer 18

yes

Answer 19

you can do this part right?

Answer 20

yes i got x=1.428

Answer 21

leave the calculator out of it

Answer 22

\[x=\frac{ 20 }{ 14 } \]

Answer 23

ok reduce!

Answer 24

what do you mean?

Answer 25

what do you mean what do i mean? reduce the fraction

Answer 26

lol what does it mean to reduce a fraction?

Answer 27

\[\frac{20}{14}=\frac{10}{7}\]

Answer 28

oh gotcha

Answer 29

ok so \[x=\frac{ 10 }{ 7 }\]

Answer 30

and since \(\frac{10}{7}>\frac{4}{5}\) that answer is good

Answer 31

now solve
\[16-20x=6x+4\]

Answer 32

wait where did we get \[\frac{ 4 }{ 5 }\] from?

Answer 33

aah i knew that might confuse you

Answer 34

:(

Answer 35

i am going to say it in english writing little or no math
the absolute value of something is either that thing, or its negative
for example the absolute value of 5 is 5 and the absolute value of minus 6 is 6
now we had the absolute value of \(20x-16\) which could be \(20x-16\) if \(20x-16\) is positive
\{20x-16\) is positive if \(x>\frac{4}{5}\)

Answer 36

last line should read \(20x-16\) is positive if \(x>\frac{4}{5}\)

Answer 37

we solved
\[20x-16=6x+4\] and got
\[\frac{10}{7}\] but once we got that we had to check that
\[\frac{10}{7}>\frac{4}{5}\] otherwise the answer would be wrong

Answer 38

thank you, i get that part but i'm asking where did 4/5 come from?

Answer 39

oh i solved

\[20x-16>0\] in one step in my head and got \[x>\frac{4}{5}\]

Answer 40

now you have to solve
\[16-20x=6x+4\] and you will bedone

Answer 41

let me know when you get
\[x=\frac{6}{13}\]

Answer 42

\x=-\frac{ 6 }{ 7 }\]

Answer 43

nope

Answer 44

i mean i got \[-\frac{ 6 }{ 7}\]

Answer 45

still nope

Answer 46

wanna try again or should i do it?

Answer 47

oh lol its x=\[\frac{ 6 }{ 13 }\]

Answer 48

yes it is
nicely reduced too (whatever that means...)

Answer 49

LOL

Answer 50

okay so all my work is mixed up so

Answer 51

im not really sure what to do next

Answer 52

we did both cases

Answer 53

x=6/13 and x=10/7

Answer 54

x=6/13,10/7

Answer 55

thats what i got

Answer 56

do u have any other questions

Answer 57

so thats the answer?

Answer 58

yes x=6/13,10/7