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 x21<0,x^2-1 < 0, which is equivalent to (x+1)(x1)<0.(x+1)(x-1) < 0. The equation (x+1)(x1)=0(x+1)(x-1) =0 has two roots x1=1, x2=1.x_1=-1,\ x_2=1.

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







Since (2)21=3>0, 021=1<0,(-2)^2-1=3>0,\ 0^2-1=-1<0, and 221=3>0,2^2-1=3>0, we conclude that the solutions of the inequality belongs to the real interval (1,1).(-1,1).

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