SOLUTION: Is there any solution to this problem? 8<9x+7<3 If not, why?

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Question 953228: Is there any solution to this problem?
8<9x+7<3
If not, why?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+8+%3C+9x+%2B+7+%3C+3+
I can state this as 2 inequalities
(1) +8+%3C+9x+%2B+7+
(2) +9x+%2B+7+%3C+3+
--------------------
(1) +8+%3C+9x+%2B+7+
Subtract +7+ from both sides
(1) +1+%3C+9x+
Divide both sides by +9+
(1) +x+%3E+1%2F9+
--------------------------
(2) +9x+%2B+7+%3C+3+
Subtract +7+ from both sides
(2) +9x+%3C+-4+
(2) +x+%3C+-4%2F9+
-----------------
There is no solution for +x+
because both inequalities cannot
be true at the same time
-----------------------
If +x+=+2%2F9+, then
+x+%3E+1%2F9+ is satisfied
+8+%3C+9%2A%282%2F9%29+%2B+7+%3C+3+
+8+%3C+9+%3C+3+ is not true
------------------------
If +x+=+-5%2F9+
+x+%3C+-4%2F9+ is satisfied
+8+%3C+9%2A%28-5%2F9%29+%2B+7+%3C+3+
+8+%3C+2+%3C+3+ is not true