Question 178221


{{{abs(2x-1)+1<6}}} Start with the given inequality



{{{abs(2x-1)<5}}} Subtract 1 from both sides.



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


{{{2x-1 > -5}}} and {{{2x-1 < 5}}} Break up the absolute value inequality using the given rule



{{{-5 < 2x-1 < 5}}} Combine the two inequalities to get a compound inequality




{{{-4 < 2x < 6}}} Add 1 to  all sides



{{{-2 < x < 3}}}  Divide all sides by 2 to isolate x




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Answer:


So our answer is


{{{-2 < x < 3}}}




which looks like this in interval notation



*[Tex \LARGE \left(-2,3\right)]



if you wanted to graph the solution set on a number line, you would get


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -9.5, 10.5),

blue(line(-2,-7,2.15,-7)),
blue(line(-2,-6,2.15,-6)),
blue(line(-2,-5,2.15,-5)),

circle(-2.5,-5.8,0.35),
circle(-2.5,-5.8,0.4),
circle(-2.5,-5.8,0.45),


circle(2.5,-5.8,0.35),
circle(2.5,-5.8,0.4),
circle(2.5,-5.8,0.45)




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