Question 119121
{{{3*abs(2x-4)-5<7}}} Start with the given inequality



{{{3*abs(2x-4)<12}}} Add 5 to both sides.



{{{abs(2x-4)<4}}} Divide both sides by 3





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


{{{2x-4 > -4}}} and {{{2x-4 < 4}}} Break up the absolute value inequality using the given rule



{{{-4 < 2x-4 < 4}}} Combine the two inequalities to get a compound inequality




{{{0 < 2x < 8}}} Add 4 to  all sides



{{{0 < x < 4}}}  Divide all sides by 2 to isolate x




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Answer:


So our answer is


{{{0 < x < 4}}}




which looks like this in interval notation



*[Tex \LARGE \left(0,4\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(-1.5,-7,1.65,-7)),
blue(line(-1.5,-6,1.65,-6)),
blue(line(-1.5,-5,1.65,-5)),

circle(-2,-5.8,0.35),
circle(-2,-5.8,0.4),
circle(-2,-5.8,0.45),


circle(2,-5.8,0.35),
circle(2,-5.8,0.4),
circle(2,-5.8,0.45)




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