Expert: Bobby Soltani - 7/6/2005

Question
If 2-3x>-1 and x+5>0, then x could equal each of the following except -4, -2, 0, or -5. Which one does x not equal?

Answer
Hi Emma,

Let's solve the two inequalities first..

2 - 3x > -1
subtract 2 from both sides
-3x > -3
divide both sides by -3 (we have to change the sign of the inequality when we multiply or divide by a negative number).

x < 1

second equation:

x + 5 > 0
subract 5 from both sides
x > -5
So, we know that x is less that 1 and greater than -5.
We can write this as
-5 < x < 1
-4 is ok
-2 is ok
0 is ok
-5 is not possible, because x is greater than -5, not greater than or equal to -5.

So, the answer is -5.  Let me know if you have any questions.

Bobby