Question 118430


{{{abs(x-2)<5}}} Start with the given inequality



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


{{{x-2 > -5}}} and {{{x-2 < 5}}} Break up the absolute value inequality using the given rule



{{{-5 < x-2 < 5}}} Combine the two inequalities to get a compound inequality




{{{-3 < x < 7}}} Add 2 to  all sides



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Answer:


So our answer is


{{{-3 < x < 7}}}




which looks like this in interval notation



*[Tex \LARGE \left(-3,7\right)]



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


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -8, 12),

blue(line(-4.5,-7,4.65,-7)),
blue(line(-4.5,-6,4.65,-6)),
blue(line(-4.5,-5,4.65,-5)),

circle(-5,-5.8,0.35),
circle(-5,-5.8,0.4),
circle(-5,-5.8,0.45),


circle(5,-5.8,0.35),
circle(5,-5.8,0.4),
circle(5,-5.8,0.45)




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