Question 1203797
<font color=black size=3>
{{{-9 < 2x+7<= 19}}}


{{{-9-7 < 2x+7-7<= 19-7}}} Subtracting 7 from all sides.


{{{-16 < 2x<= 12}}}


{{{-16/2 < 2x/2<= 12/2}}} Dividing all sides by 2.


{{{-8 < x<= 6}}}


That condenses to the interval notation <font color=red size=4>(-8, 6]</font>


Use a curved parenthesis to exclude the endpoint -8.
Use a square bracket to include the endpoint 6.


The graph on a number line will have an open hole at -8 and a closed filled in endpoint at 6. Shade in between.
{{{
drawing(400,200,-6,6,-3,3,
line(-10,0,10,0),line(-5,0.04,-5,-0.04),line(-3.8889,0.04,-3.8889,-0.04),line(-2.7778,0.04,-2.7778,-0.04),line(-1.6667,0.04,-1.6667,-0.04),line(-0.5556,0.04,-0.5556,-0.04),line(0.5556,0.04,0.5556,-0.04),line(1.6667,0.04,1.6667,-0.04),line(2.7778,0.04,2.7778,-0.04),line(3.8889,0.04,3.8889,-0.04),line(5,0.04,5,-0.04),locate(-5.15,-0.25,"-10"),locate(-3.9889,-0.25,"-8"),locate(-2.8778,-0.25,"-6"),locate(-1.7667,-0.25,"-4"),locate(-0.6556,-0.25,"-2"),locate(0.5056,-0.25,"0"),locate(1.6167,-0.25,"2"),locate(2.7278,-0.25,"4"),locate(3.8389,-0.25,"6"),locate(4.95,-0.25,"8"),

red(
circle(-3.8889,0,0.35),
circle(-3.8889,0,0.3),
circle(-3.8889,0,0.25),
circle(-3.8889,0,0.2),
line(-3.8889+0.1,0.1,3.8389,0.1),
line(-3.8889+0.2,0.05,3.8389,0.05),
line(-3.8889+0.2,0,3.8389,0),
line(-3.8889+0.2,-0.05,3.8389,-0.05),
line(-3.8889+0.1,-0.1,3.8389,-0.1),
circle(3.8889,0,0.3),
circle(3.8889,0,0.25),
circle(3.8889,0,0.2),
circle(3.8889,0,0.15),
circle(3.8889,0,0.1),
circle(3.8889,0,0.05),
circle(3.8889,0,0.02)
)
)
}}}
</font>