Question 208185


{{{abs(2x-4)<6}}} Start with the given inequality



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


{{{2x-4 > -6}}} and {{{2x-4 < 6}}} Break up the absolute value inequality using the given rule



{{{-6 < 2x-4 < 6}}} Combine the two inequalities to get a compound inequality




{{{-2 < 2x < 10}}} Add 4 to  all sides



{{{-1 < x < 5}}}  Divide all sides by 2 to isolate x




----------------------------------------------------


Answer:


So our answer is


{{{-1 < x < 5}}}




which looks like this in interval notation



*[Tex \LARGE \left(-1,5\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(-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