Question 150967
{{{-168 < 11x - 14 < = 8}}} Start with the given compound inequality.



{{{-168+ 14 < 11x +cross(-14+14)  < = 8+ 14}}} Add 14 to all sides.



{{{-154<11x<=22}}} Combine like terms.



{{{-154/11<cross(11/11)x<=22/11}}} Divide all sides by 11.



{{{-14<x<=2}}} Divide.


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Answer:


So the solution set is 


{{{-14<x<=2}}}



So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-14,2}]<font size="8">]</font>



So the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-14 < x \le 2\right\}]



Here's the graph of the solution set


{{{drawing(500,80,-19, 7,-10, 10,
number_line( 500, -19, 7 ,2),

blue(line(-14,0,2,0)),
blue(line(-14,0.30,2,0.30)),
blue(line(-14,0.15,2,0.15)),
blue(line(-14,-0.15,2,-0.15)),
blue(line(-14,-0.30,2,-0.30)),
circle(-14,0,0.3),circle(-14,0,0.35)

)}}} Graph of the solution set


Note:

There is an <b>open</b> circle at {{{x=-14}}} which means that we're excluding this value from the solution set

Also, there is a <b>closed</b> circle at {{{x=2}}} which means that we're including this value in the solution set.