anonymous
  • anonymous
Determine solution set of the inequality \[|x-1|\geq 3|x+1|\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i think you need to work in cases if \(x>1\) then \(|x-1|=x-1\) and \(|x+1|=x+1\) first job it to solve \[x-1\geq 3(x+1)\]
anonymous
  • anonymous
if \(x<-1\) then \(|x-1=1-x\) and \(|x+1|=-x-1\) etc
anonymous
  • anonymous
the solution is -2

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anonymous
  • anonymous
ok lets go slow
anonymous
  • anonymous
ok..
anonymous
  • anonymous
if \(x>1\) then both \(x-1\) and \(x+1\) are positive, right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
which means they are equal to their absolute values in other words \(|x+1|=x+1\) and \(|x-1|=x-1\)
anonymous
  • anonymous
so if \(x>1\) you need to solve \[x-1\geq 3(x+1)\]
anonymous
  • anonymous
we solve in a couple of steps \[x-1\geq 3x+3\]\[-1\geq 2x+3 \\-4\geq 2x \\x<-2\] but here we have a problem because we were assuming that \(x>1\) but came up with \(x<-2\) so if \(x>1\) there is NO solution
anonymous
  • anonymous
now we try again with \[x<-1\] but this time both \(x-1\) and \(x+1\) are negative, and so \[|x+1|=-x-1\] and \[|x-1|=-x+1\]
anonymous
  • anonymous
we solve \[-x+1\geq 3(-x-1)\] in the same number of steps \[-x+1\geq -3x-3\] \[2x+1\geq -3\] \[2x\geq -4\] \[x\geq -2\]
anonymous
  • anonymous
that means if \(x<-1\) then also \(x>-2\) so we know we are good from \(-2\) up to \(-1\)
anonymous
  • anonymous
thanks Satellite, what about 1/2 we still didn't get it..
anonymous
  • anonymous
(sorry i got internet problem before)

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