Question 935604
The given inequality has the square root restriction that {{{x>=-3}}}, and further arithmetic {{{(x+3)^(1/2)-x+1>0}}} with steps (starts with squaring both sides) that lead to {{{x^2-3x-2}}} gives two further critical values for x:


Using general solution for a quadratic equation:
Roots  {{{(3-sqrt(17))/2}}} and {{{(3+sqrt(17))/2}}}.
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<x<-0.275}}}_____________TRUE
{{{-0.275<x<3.56155}}}________TRUE
{{{3.56155<x}}}_______________FALSE



Graph should be like this:
{{{graph(300,300,-4,4,-10,10,(x+3)^(1/2)-x+1)}}}