Question 165210
{{{-3<x+2<7}}} Start with the given compound inequality.



{{{-3-2<x<7-2}}} Subtract {{{2}}} from ALL sides.



{{{-5<x<7-2}}} Combine like terms on the left side.



{{{-5<x<5}}} Combine like terms on the right side.



So our answer is {{{-5<x<5}}}



So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-5,5}]<font size="8">)</font>



So the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-5 < x < 5\right\}]



Here's the graph of the solution set


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

blue(line(-5,0,5,0)),
blue(line(-5,0.30,5,0.30)),
blue(line(-5,0.15,5,0.15)),
blue(line(-5,-0.15,5,-0.15)),
blue(line(-5,-0.30,5,-0.30)),
circle(-5,0,0.25),circle(-5,0,0.20),
circle(5,0,0.25),
circle(5,0,0.20)

)}}} Graph of the solution set


Note:

There is an <b>open</b> circle at {{{x=-5}}} which means that we're excluding this value from the solution set

Also, there is an <b>open</b> circle at {{{x=5}}} which means that we're excluding this value from the solution set.