Question 350698
We essentially want to solve {{{abs(x+5)>8}}}



{{{abs(x+5)>8}}} Start with the given inequality



Break up the absolute value (remember, if you have {{{abs(x)> a}}}, then {{{x < -a}}} or {{{x > a}}})


{{{x+5 < -8}}} or {{{x+5 > 8}}} Break up the absolute value inequality using the given rule





Now lets focus on the first inequality  {{{x+5 < -8}}}



{{{x+5<-8}}} Start with the given inequality



{{{x<-8-5}}}Subtract 5 from both sides



{{{x<-13}}} Combine like terms on the right side



Now lets focus on the second inequality  {{{x+5 > 8}}}



{{{x+5>8}}} Start with the given inequality



{{{x>8-5}}}Subtract 5 from both sides



{{{x>3}}} Combine like terms on the right side




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Answer:


So our answer is


{{{x < -13}}} or {{{x > 3}}}



which looks like this in interval notation



*[Tex \LARGE \left(-\infty,-13\right)\cup\left(3,\infty\right)]


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Jim