Question

Polynomial Inequalities:

6) x^2 - 1 < 0

show number line test and answer in interval notation

Answer 1

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 $(-1,1).$