Question 182032


{{{-7<3x+2<=14}}} Start with the given compound inequality.



{{{-7-2<3x<=14-2}}} Subtract {{{2}}} from all sides.



{{{-9<3x<=14-2}}} Combine like terms on the left side.



{{{-9<3x<=12}}} Combine like terms on the right side.



{{{(-9)/3<x<=(12)/3}}} Divide all sides by 3.



{{{-3<x<=4}}} Reduce.



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Answer:


So the solution is {{{-3<x<=4}}}



So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-3,4}]<font size="8">]</font>



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-3 < x \le 4\right\}]



Here's the graph of the solution set


{{{drawing(500,80,-8, 9,-10, 10,
number_line( 500, -8, 9 ,4),

blue(line(-3,0,4,0)),
blue(line(-3,0.30,4,0.30)),
blue(line(-3,0.15,4,0.15)),
blue(line(-3,-0.15,4,-0.15)),
blue(line(-3,-0.30,4,-0.30)),
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=-3}}} which means that we're excluding this value from the solution set

Also, there is a <b>closed</b> circle at {{{x=4}}} which means that we're including this value in the solution set.