Reiny - the problem with the different inequality signs was typed from the textbook. I will notify instructor Thanks

Question

Another problem
3<5x-27<53
1st part
3<5x-27
27+3<5x-27+27
30/5 < 5x/5
6<x

2nd part
5x-27<53
5x-27+27<53+27
5x/5 < 80/5
x<16

combine 6<x<16

Am I correct?

Answer 1

you can do both at once

3 < 5x-27 < 53
30 < 5x < 80
6 < x < 16

Answer 2

the nice thing about having the orientation of the inequality signs going the same way is that you can just perform the solution as it stands

3<5x-27<53
you are trying to get just "x" in the middle, so
add 27 to all parts

30 < 5x < 80
divide by +5

6 < x < 16 , same as yours

Now wasn't that easy, just took 2 steps.
That is why the orientation of the signs going the same way is so important.

Answer 3

Thanks