SOLUTION: How do I solve this inequality? {{{7/(x+1) > 7}}}

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Question 913462: How do I solve this inequality?
7%2F%28x%2B1%29+%3E+7

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Make all numbers onto one side of the order relation.

7%2F%28x%2B1%29-7%3E0

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

%281-%28x%2B1%29%29%2F%28x%2B1%29%3E0

-x%2F%28x%2B1%29%3E0
The critical values are x at 0 and -1. These form three intervals for the real x number line.

(-infinity, -1)
Pick any value, example, -3.
-%28-3%29%2F%28-3%2B1%29
3%2F%28-2%29
-3%2F2%3E0
FALSE.

(-1, 0)
Pick some value, -1/2.
-%28-1%2F2%29%2F%28-1%2F2%2B1%29
%281%2F2%29%2F%281%2F2%29
1%3E0
TRUE.

(0, infinity)
Pick a value greater than 0, like 1.
-1%2F%281%2B1%29
-1%2F2%3E0
FALSE.

One more thing: The original inequality seems to have no restriction for x at 0; so maybe x=0 might work. Check this.
7%2F%280%2B1%29%3E7 ?
7%2F1%3E7
7%3E7
FALSE!

RESULT, ANSWER: highlight%28highlight%28-1%3Cx%3C0%29%29