Question 169788


{{{-2<a+3<8}}} Start with the given compound inequality.



{{{-2-3<a<8-3}}} Subtract {{{3}}} from all sides.



{{{-5<a<8-3}}} Combine like terms on the left side.



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



So the answer is {{{-5<a<5}}}





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



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{a\|-5 < a < 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 {{{a=-5}}} which means that we're excluding this value from the solution set

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