Question 341660
{{{abs(6y-2)+4<22}}} Start with the given inequality



{{{abs(6y-2)<18}}} Subtract 4 from both sides.



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


{{{6y-2 > -18}}} and {{{6y-2 < 18}}} Break up the absolute value inequality using the given rule



{{{-18 < 6y-2 < 18}}} Combine the two inequalities to get a compound inequality




{{{-16 < 6y < 20}}} Add 2 to  all sides



{{{-8/3 < y < 10/3}}}  Divide all sides by 6 to isolate y




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Answer:


So our answer is


{{{-8/3 < y < 10/3}}}




which looks like this in interval notation



*[Tex \LARGE \left(-\frac{8}{3},\frac{10}{3}\right)]



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


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -9.66666666666667, 10.3333333333333),

blue(line(-2.5,-7,2.65,-7)),
blue(line(-2.5,-6,2.65,-6)),
blue(line(-2.5,-5,2.65,-5)),

circle(-3,-5.8,0.35),
circle(-3,-5.8,0.4),
circle(-3,-5.8,0.45),


circle(3,-5.8,0.35),
circle(3,-5.8,0.4),
circle(3,-5.8,0.45)




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



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Jim