SOLUTION: The solution of the inequality sqrt( 5-x ) < x+1 is (a) < x &#8804; (b) What are a and b?

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Question 878378: The solution of the inequality sqrt( 5-x ) < x+1 is (a) < x ≤ (b)
What are a and b?
Found 2 solutions by josgarithmetic, Fombitz:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
After trying to answer this one and finding that x is not between any two domain values, the inequality does not conform to what you want. The only meaningful critical point is x=1. The inequality becomes true for x<1. Your "b" is 1. The statement has no specific value as a cutoff for "a".

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285-x%29%3Cx%2B1
5-x%3Cx%5E2%2B2x%2B1
x%5E2%2B3x-4%3E0
%28x%2B4%29%28x-1%29%3E0
The solution for this is x%3C-4 and x%3E1.
However the negative solutions do not solve the equation, they only do so when the two sides are squared so only x%3E1 is accepted as a solution.
.
.
.
In addition, we have an additional constraint with the square root function.
5-x%3E=0
x%3C=5
So putting those together, the solution region is,
1%3Cx%3C=5