Question

Find the absolute value inequality of 8-/2x-5/<3

Answer 1

does this say
\[8-|2x-5|<3\]??

Answer 2

if so, rearrange to get
\[8-3<|2x-5|\]
\[5<|2x-5|\] and then solve that one

Answer 3

8-/2x-5/<3

Answer 4

\[5<|2x-5|\] means
\[2x-5>5\] or
\[2x-5<-5\]
solve separately, get two separate intervals

Answer 5

Thanks a lot

Answer 6

My solution is -/2x-5/<3-8

Answer 7

Which is 5<-2x-5<-5

Answer 8

I mean 5<-2x+5<-5

Answer 9

hold the phone

Answer 10

you cannot have a compound inequality like that, because you have 5 on the left being smaller than -5 on the right, there is no such thing as
\[5<a<-5\]

Answer 11

the answer is two separate intervals, and it comes from two separate inequalities. namely
\[5<2x-5\]
\[10<2x\]
\[5<x\] i.e. \(x\) is larger than 5 OR
\[2x-5<-5\]
\[2x<0\]
\[x<0\] i.e. \(x\) is less that 0 (aka negative) so your answer should be two separate inequalities,
\[x<0\text{ or } x>5\]

Answer 12

So -/2x-5/<3-8
-(2x-5)<-5

Answer 13

\(-|2x-5|<-5\iff |2x-5|>5\)

Answer 14

Sorry for laye reply. What I was thingking if it is absolute value like -/2x-5/ it will be -(2x-5) so -2x+5<-5 and -2x+5<5