Question 130973
Does your problem look like this: {{{abs(x)>6}}} ???






{{{abs(x)>6}}} Start with the given inequality



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


{{{x < -6}}} or {{{x > 6}}} Break up the absolute value inequality using the given rule





So our solution is simply



{{{x < -6}}} or {{{x > 6}}}



which looks like this in interval notation



*[Tex \LARGE \left(-\infty,-6\right)\cup\left(6,\infty\right)]



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


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -10, 10),

blue(arrow(-6.5,-7,-10,-7)),
blue(arrow(-6.5,-6.5,-10,-6.5)),
blue(arrow(-6.5,-6,-10,-6)),
blue(arrow(-6.5,-5.5,-10,-5.5)),
blue(arrow(-6.5,-5,-10,-5)),
blue(arrow(6.5,-7,10,-7)),
blue(arrow(6.5,-6.5,10,-6.5)),
blue(arrow(6.5,-6,10,-6)),
blue(arrow(6.5,-5.5,10,-5.5)),
blue(arrow(6.5,-5,10,-5)),

circle(-6,-5.8,0.35),
circle(-6,-5.8,0.4),
circle(-6,-5.8,0.45),


circle(6,-5.8,0.35),
circle(6,-5.8,0.4),
circle(6,-5.8,0.45)




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