Question

(help!!) Solve the compound inequality.
36 ≥ 1-5z > -21

Answer 1

Start off by clearing off the 1...subtract 1 from all sides, leaving 35<-5z<-22

Answer 2

Now, divide by -5 and get -7>z>22/5

Answer 3

Split the compound inequality into two inequalities:
\[36\ge(1-5z)\]
and
\[(1-5z)>-21\]

Answer 4

solve each inequality separately
\[36\ge(1-5z)\]
subtract one from each side, then divide by (-5) from each side and flip the direction of the inequality sign since we are dividing by a negative.
\[35\ge(-5z)\]
\[-7\le z\]

Answer 5

Do the same for the other inequality
subtract one and then divide by (-5) and switch the direction of the inequality sign
\[(1-5z)>-21\]
\[(-5z)>-22\]
\[z<\frac{ 22 }{ 5 }\]

Answer 6

just realized the original process given by OakTree is fine except that it started with the inequality signs pointing the wrong way.
\[-7\le z < \frac{ 22 }{ 5 }\]

Answer 7

@juantweaver Ohhhh thank you so much!!! :) Really appreciate it. I see now :) I wasn't sure to leave it as a fraction or if i needed to subtract the one but now I understand, thanks :)

Answer 8

& You're the best for showing all the steps so I could understand! Thank you :) I was on the right track!