SOLUTION: Solve the inequality (x+3)^1/2 > x-1.Show also the graph.

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Question 935604: Solve the inequality (x+3)^1/2 > x-1.Show also the graph.
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20855) About Me  (Show Source):
Answer by josgarithmetic(39800) About Me  (Show Source):
You can put this solution on YOUR website!
The given inequality has the square root restriction that x%3E=-3, and further arithmetic %28x%2B3%29%5E%281%2F2%29-x%2B1%3E0 with steps (starts with squaring both sides) that lead to x%5E2-3x-2 gives two further critical values for x:

Using general solution for a quadratic equation:
Roots %283-sqrt%2817%29%29%2F2 and %283%2Bsqrt%2817%29%29%2F2.
Those are near -0.275 and 3.56155.

If you will check the intervals and find truth or falseness of the GIVEN inequality, find like this:

INTERVAL________________INEQUALITY?
-3%3Cx%3C-0.275_____________TRUE
-0.275%3Cx%3C3.56155________TRUE
3.56155%3Cx_______________FALSE


Graph should be like this:
graph%28300%2C300%2C-4%2C4%2C-10%2C10%2C%28x%2B3%29%5E%281%2F2%29-x%2B1%29