The tutor above points out something that I have long known.
It is virtually impossible to successfully teach students to write
mathematics containing fractions correctly all on one line.
You wrote this:
4/x+2 > 2
which means this , which is the way the tutor took
it.
However I reason that since you are taking a higher level of
algebra, your teacher would not be testing you to see if you are
able to do a simple thing like the first step would require, to
subtract 2 from both sides to get
Therefore I assume that you meant this:
instead, which when written on one line would require parentheses
around the denominator; otherwise the +2 will not be taken as part
of the denominator but will be taken as a separate term. So it
should be written this way:
4/(x+2) > 2
------------------------------
We find the critical numbers by setting
numerator = 0 and denominator = 0
2x = 0; x+2 = 0
x = 0; x = -2
[Note: These critical numbers are NOT permissible values of x]
We place the critical numbers on a number line:
-------o-----o------------
-4 -3 -2 -1 0 1 2 3 4
We test a value for x left of -2, say -3 in this:
That's false so we do not shade left of -2
We test a value for x between -2 and 0, say -1 in this:
That's true so we shade between -2 and 0.
-------o=====o------------
-4 -3 -2 -1 0 1 2 3 4
We test a value for x right of 0, say 1 in this:
This is false so we do not shade to the right of 0.
Answer {x | -2 < x < 0} in set-builder notation
or (-2,0) in interval notation.
Edwin
(