SOLUTION: Solve the compound inequality: -25 less than or equal to -4x+5 less than or equal to 37

Question 1038795: Solve the compound inequality:
-25 less than or equal to -4x+5 less than or equal to 37
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
-25 <-4x+5 < 37
Just like any other math problem, you try to isolate the variable. Therefore, you are adding 5, so to isolate the x, let's subtract 5...
-25 <-4x+5 < 37
-5 ...... -5 ...... -5
_________________
-30 < -4x < 32
(Please excuse the dots. I'm trying to move the numbers on the page, but they don't move if I only hit the space bar).
Ok we still need to isolate the x, so you can see that -4 must be "Separated" from the x, so, since -4 is multiplied with x, let's UN-do that multiplication by dividing by -4.
BUT! This is important. When you divide or multiply by a negative number in an inequality, you must FLIP the sign.

SO! We have this:
-30 < -4x < 32
---- ---- ---
-4 ... -4 ... -4
this gives us:
> x > -8
See how the signs are flipped??
Please also note that it is NEGATIVE 30 divided by NEGATIVE 4 results in a positive number. Remember that a negative divided by a negative is a positive. :-) Likewise, negative 32 divided by negative 4 is negative 8.
We can reduce the fraction to:
> x > -8
The inequalities should be greater than or equal to, but I didn't know how to make those signs show up on this page. The way of doing the work is correct, but you just have to put those signs in yourself.
I hope this helps!

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