SOLUTION: {{{ 9/(h+1) > 9 }}} Solve the inequality. After finding the important values/zeroes (-1 and 0) I checked -2, -.5, and 1 using the equation {{{ 9 > 9h+9 }}}and {{{ 0 > 9h }}}

Algebra ->  Rational-functions -> SOLUTION: {{{ 9/(h+1) > 9 }}} Solve the inequality. After finding the important values/zeroes (-1 and 0) I checked -2, -.5, and 1 using the equation {{{ 9 > 9h+9 }}}and {{{ 0 > 9h }}}      Log On


   

Question 976979: +9%2F%28h%2B1%29+%3E+9+
Solve the inequality.
After finding the important values/zeroes (-1 and 0)
I checked -2, -.5, and 1 using the equation +9+%3E+9h%2B9+and +0+%3E+9h+
When plugged into these inequalities -2 and -.5 worked, however when plugged into the original equation only -.5 worked.
Why did -2 not work despite it working in the above inequalities that I consider to be the same?
Also sorry if this was supposed to be posted in inequalities rather than rational functions.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
First, multiply left and right by %281%2F9%29.

1%2F%28h%2B1%29%3E1

Continuing,

1%2F%28h%2B1%29-1%3E0

1%2F%28h%2B1%29-%28h%2B1%29%2F%28h%2B1%29%3E0

highlight_green%28h%2F%28h%2B1%29%3E0%29
The critical values are the root which is 0, and the undefined value which is -1. These form the intervals on h of h%3C-1, -1%3Ch%3C0, and 0%3Ch. CHECK ANY ONE VALUE in each interval and determine if the value and the interval will work in the ORIGINAL inequality.

Write again if any trouble doing that.

Answer by MathTherapy(10810) About Me  (Show Source):
You can put this solution on YOUR website!
+9%2F%28h%2B1%29+%3E+9+
Solve the inequality.
After finding the important values/zeroes (-1 and 0)
I checked -2, -.5, and 1 using the equation +9+%3E+9h%2B9+and +0+%3E+9h+
When plugged into these inequalities -2 and -.5 worked, however when plugged into the original equation only -.5 worked.
Why did -2 not work despite it working in the above inequalities that I consider to be the same?
Also sorry if this was supposed to be posted in inequalities rather than rational functions.
You're correct: h+%3C+0, and h+%3C%3E+-+1

Thus, there are 2 intervals to check: h+%3C+-+1, and -+1+%3C+h+%3C+0. You'll see that only those

values in the interval: highlight_green%28-+1+%3C+h+%3C+0%29 work.

By the way, h+=+-+2 DOES NOT make the inequality true, so that value is not in the interval 

of values that satisfy the inequality.