Question 158220
{{{abs(x+5)>12}}} 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 < -12}}} or {{{x+5 > 12}}} Break up the absolute value inequality using the given rule





Now lets focus on the first inequality  {{{x+5 < -12}}}



{{{x+5<-12}}} Start with the given inequality



{{{x<-12-5}}}Subtract 5 from both sides



{{{x<-17}}} Combine like terms on the right side



Now lets focus on the second inequality  {{{x+5 > 12}}}



{{{x+5>12}}} Start with the given inequality



{{{x>12-5}}}Subtract 5 from both sides



{{{x>7}}} Combine like terms on the right side




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Answer:


So our answer is


{{{x < -17}}} or {{{x > 7}}}



which looks like this in interval notation



*[Tex \LARGE \left(-\infty,-17\right)\cup\left(7,\infty\right)]



if you wanted to graph the solution set, you would get


{{{drawing(500,80,-22, 12,-10, 10,
number_line( 500, -22, 12 ),


circle(-17,0,0.45),
circle(-17,0,0.40),


blue(arrow(-17,0,-22,0)),
blue(arrow(-17,0.30,-22,0.30)),
blue(arrow(-17,0.15,-22,0.15)),
blue(arrow(-17,-0.15,-22,-0.15)),
blue(arrow(-17,-0.30,-22,-0.30)),



circle(7,0,0.45),
circle(7,0,0.40),


blue(arrow(7,0,12,0)),
blue(arrow(7,0.30,12,0.30)),
blue(arrow(7,0.15,12,0.15)),
blue(arrow(7,-0.15,12,-0.15)),
blue(arrow(7,-0.30,12,-0.30))


)}}} Graph of the solution set in blue and the excluded values represented by open circles