SOLUTION: solve the inequality. give the result in set notation and graph it 4<-z-4<11 would appreciate some kindly heplp

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Question 1106901: solve the inequality. give the result in set notation and graph it 4<-z-4<11
would appreciate some kindly heplp

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


4<-z-4<11

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.

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.

4+%3C+-z-4+%3C+11
-4+%3E+z%2B4+%3E+-11 multiply by -1; change the direction of the inequality
-11+%3C+z%2B4+%3C+-4 rewrite the inequality in standard form -- with the lower bound on the left and the upper bound on the right
-15+%3C+z+%3C+-8 subtract 4 to get z by itself

OR...

4+%3C+-z-4+%3C+11
8+%3C+-z+%3C+15 add 4 to get "-z" by itself in the middle
-8+%3E+z+%3E+-15 multiply by -1 to get z in the middle
-15+%3C+z+%3C+-8 rewrite in standard form

You can put the result in set notation and draw the graph yourself....