Question 113266


{{{abs(2b-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}}})


{{{2b-5 < -8}}} or {{{2b-5 > 8}}} Break up the absolute value inequality using the given rule





Now lets focus on the first inequality  {{{2b-5 < -8}}}



{{{2b-5<-8}}} Start with the given inequality



{{{2b<-8+5}}}Add 5 to both sides



{{{2b<-3}}} Combine like terms on the right side



{{{b<(-3)/(2)}}} Divide both sides by 2 to isolate b 




{{{b<-3/2}}} Reduce



Now lets focus on the second inequality  {{{2b-5 > 8}}}



{{{2b-5>8}}} Start with the given inequality



{{{2b>8+5}}}Add 5 to both sides



{{{2b>13}}} Combine like terms on the right side



{{{b>(13)/(2)}}} Divide both sides by 2 to isolate b 




{{{b>13/2}}} Reduce




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Answer:


So our answer is


{{{b < -3/2}}} or {{{b > 13/2}}}



which looks like this in interval notation



*[Tex \LARGE \left(-\infty,\frac{-3}{2}\right)\cup\left(\frac{13}{2},\infty\right)]



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


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -7.5, 12.5),

blue(arrow(-4.5,-7,-10,-7)),
blue(arrow(-4.5,-6.5,-10,-6.5)),
blue(arrow(-4.5,-6,-10,-6)),
blue(arrow(-4.5,-5.5,-10,-5.5)),
blue(arrow(-4.5,-5,-10,-5)),
blue(arrow(4.5,-7,10,-7)),
blue(arrow(4.5,-6.5,10,-6.5)),
blue(arrow(4.5,-6,10,-6)),
blue(arrow(4.5,-5.5,10,-5.5)),
blue(arrow(4.5,-5,10,-5)),

circle(-4,-5.8,0.35),
circle(-4,-5.8,0.4),
circle(-4,-5.8,0.45),


circle(4,-5.8,0.35),
circle(4,-5.8,0.4),
circle(4,-5.8,0.45)




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