Question 117759


{{{-6<=3+x<4}}} Start with the given inequality






{{{-9<=x<1}}} Subtract 3 from all sides



So the solution in interval notation is: [-9,1)



Now let's graph the solution set


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -14, 6),
blue(line(-4.75,-7,4.85,-7)),
blue(line(-4.75,-6,4.85,-6)),
blue(line(-4.75,-5,4.85,-5)),

circle(-5,-5.8,0.10),
circle(-5,-5.8,0.15),
circle(-5,-5.8,0.2),
circle(-5,-5.8,0.25),
circle(-5,-5.8,0.35),
circle(-5,-5.8,0.4),

circle(5,-5.8,0.35),
circle(5,-5.8,0.4),
circle(5,-5.8,0.45)


)}}}


Note: at {{{x=-9}}} there is a <font size="4"><b>closed</b></font>  circle (which means this point is included) and at {{{x=1}}} there is a <font size="4"><b>open</b></font> circle (which means this point is excluded)