Question 151744


{{{-6<x+3<6}}} Start with the given compound inequality.



{{{-6-3<x<6-3}}} Subtract {{{3}}} from all sides.



{{{-9<x<6-3}}} Combine like terms on the left side.



{{{-9<x<3}}} Combine like terms on the right side.



So our answer is {{{-9<x<3}}}



So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-9,3}]<font size="8">)</font>



So the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-9 < x < 3\right\}]



Here's the graph of the solution set


{{{drawing(500,80,-14, 8,-10, 10,
number_line( 500, -14, 8 ),

blue(line(-9,0,3,0)),
blue(line(-9,0.30,3,0.30)),
blue(line(-9,0.15,3,0.15)),
blue(line(-9,-0.15,3,-0.15)),
blue(line(-9,-0.30,3,-0.30)),
circle(-9,0,0.25),circle(-9,0,0.20),
circle(3,0,0.25),
circle(3,0,0.20)

)}}} Graph of the solution set


Note:

There is an <b>open</b> circle at {{{x=-9}}} which means that we're excluding this value from the solution set

Also, there is an <b>open</b> circle at {{{x=3}}} which means that we're excluding this value from the solution set.