Question 174310


{{{abs(2x+4)<8}}} 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 > -8}}} and {{{2x+4 < 8}}} Break up the absolute value inequality using the given rule



{{{-8 < 2x+4 < 8}}} Combine the two inequalities to get a compound inequality




{{{-12 < 2x < 4}}} Subtract 4 from  all sides



{{{-6 < x < 2}}}  Divide all sides by 2 to isolate x




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Answer:


So our answer is


{{{-6 < x < 2}}}




which looks like this in interval notation



*[Tex \LARGE \left(-6,2\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, -12, 8),

blue(line(-3.5,-7,3.65,-7)),
blue(line(-3.5,-6,3.65,-6)),
blue(line(-3.5,-5,3.65,-5)),

circle(-4,-5.8,0.35),
circle(-4,-5.8,0.4),
circle(-4,-5.8,0.45),


circle(4,-5.8,0.35),
circle(4,-5.8,0.4),
circle(4,-5.8,0.45)




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