Question 1106901
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4<-z-4<11<br>
We need to get "z" by itself in the middle of the compound inequality.  So at some point we will need to multiply the whole inequality by -1, which means the direction of the inequality changes.<br>
In this case we can do either of two things first: multiply by -1, or get rid of the "-4" in the middle.  Let's do it both ways, for practice, and to see that we get the same answer.<br>
{{{4 < -z-4 < 11}}}
{{{-4 > z+4 > -11}}}  multiply by -1; change the direction of the inequality
{{{-11 < z+4 < -4}}}  rewrite the inequality in standard form -- with the lower bound on the left and the upper bound on the right
{{{-15 < z < -8}}}  subtract 4 to get z by itself<br>
OR...<br>
{{{4 < -z-4 < 11}}}
{{{8 < -z < 15}}}  add 4 to get "-z" by itself in the middle
{{{-8 > z > -15}}}  multiply by -1 to get z in the middle
{{{-15 < z < -8}}}  rewrite in standard form<br>
You can put the result in set notation and draw the graph yourself....