Answer to Question #236781 in Calculus for CCW

Question #236781

Polynomial Inequalities:

6) x^2 - 1 < 0

show number line test and answer in interval notation


1
Expert's answer
2021-09-21T11:38:24-0400

Let us solve the equality "x^2-1 < 0," which is equivalent to "(x+1)(x-1) < 0." The equation "(x+1)(x-1) =0" has two roots "x_1=-1,\\ x_2=1."

Let us use number line test. For this draw the following intervals:







Since "(-2)^2-1=3>0,\\ 0^2-1=-1<0," and "2^2-1=3>0," we conclude that the solutions of the inequality belongs to the real interval "(-1,1)."

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