Question 1038795
-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:

{{{30/4}}} > 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:

{{{15/2}}} > 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!