SOLUTION: The solution of the inequality: -x < x^2 < 2x + 1, is { ?? < x

SOLUTION: The solution of the inequality: -x < x^2 < 2x + 1, is { ?? < x < ??} Thanks in advance!

Question 860535: The solution of the inequality: -x < x^2 < 2x + 1, is { ?? < x < ??}
Thanks in advance!
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Analyze two separate inequalities.
AND ; look for what is true for both at the same time.

Critical points 0 and -1.
Solutions: OR .

discriminant, 4-4(-1)=8
roots or horiz intercepts will be the critical points:

OR
.
The parabola opens upward, and the points below the level y=0 occur BETWEEN the horizontal intercepts.

The x values common for both inequalities are , which is easier to see if you make a number line.
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