SOLUTION: Find the solution set (algebraically) to the inequality below: &#8730;(x+7)+5 < x

Algebra ->  Equations -> SOLUTION: Find the solution set (algebraically) to the inequality below: &#8730;(x+7)+5 < x      Log On


   

Question 1010356: Find the solution set (algebraically) to the inequality below:
√(x+7)+5 < x
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%28x%2B7%29%29%5E2%3C%28x-5%29%5E2

x%2B7%3Cx%5E2-10x%2B25

x%5E2-10x%2B25-x-7%3E0

x%5E2-11x%2B18%3E0

Discriminant, 121-4%2A18=49=7%5E2;
zeros are %28-11-7%29%2F2=-9 and %28-11%2B7%29%2F2=-2.
BE CAREFUL. This became a parabola, but the inequality cannot use x%3C-7, meaning neither can x%3C-9. Do you understand why? On the other side, you can use the part, highlight%28x%3E-2%29.