Question 145488



{{{4<-z-4<11}}} Start with the given inequality






{{{8<-z<15}}} Add 4 to all sides







{{{-8>z>-15}}} Divide every side by -1 to isolate z. Remember, dividing every side of an inequality by a negative number flips the inequality signs





{{{-15<z<-8}}} Rearrange the inequality.



So the solution in interval notation is: (-15,-8)



The solution in set notation is *[Tex \LARGE \left\{z\|-15<z<-8\right\}]



Now let's graph the solution set


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -21.5, -1.5),
blue(line(-3.25,-7,3.35,-7)),
blue(line(-3.25,-6,3.35,-6)),
blue(line(-3.25,-5,3.35,-5)),

circle(-3.5,-5.8,0.35),
circle(-3.5,-5.8,0.4),
circle(-3.5,-5.8,0.45),

circle(3.5,-5.8,0.35),
circle(3.5,-5.8,0.4),
circle(3.5,-5.8,0.45)


)}}}


Note: at {{{z=-15}}} there is a <font size="4"><b>open</b></font>  circle (which means this point is excluded) and at {{{z=-8}}} there is a <font size="4"><b>open</b></font> circle (which means this point is excluded)