Question 127512
{{{abs(4-x)<5}}} Start with the given inequality



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


{{{4-x > -5}}} and {{{4-x < 5}}} Break up the absolute value inequality using the given rule



{{{-5 < 4-x < 5}}} Combine the two inequalities to get a compound inequality




{{{-9 < -x < 1}}} Subtract 4 from  all sides



{{{9 > x > -1}}} Divide all sides by -1. This will isolate x. Remember, dividing by a negative number flips the inequality signs.



{{{-1<x<9}}} Rearrange the inequality


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Answer:


So our answer is


{{{-1<x<9}}}



which looks like this in interval notation



*[Tex \LARGE \left(-1,9\right)]



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


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -6, 14),

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