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Which compound inequality represents the value of $x ?$ $\newline$ (x - 1)(x + 1) > 0 $\newline$

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Solve quadratic inequalities

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Q. Which compound inequality represents the value of

x ?

\newline

(x - 1)(x + 1) > 0

\newline

Find Zeros: Find the zeros of the quadratic by setting each factor to zero. $\newline$ $x - 1 = 0$ gives $x = 1$ . $\newline$ $x + 1 = 0$ gives $x = -1$ .
Determine Intervals: Determine the intervals to test around the zeros: $(-\infty, -1)$ , $(-1, 1)$ , and $(1, \infty)$ .
Test Around Zeros: Test a value from the interval $(-\infty, -1)$ , say $x = -2$ . $\newline$ $(-2 – 1)(-2 + 1) = (-3)(-1) = 3$ , which is positive.
Combine Positive Intervals: Test a value from the interval $(-1, 1)$ , say $x = 0$ . $(0 - 1)(0 + 1) = (-1)(1) = -1$ , which is negative.
Combine Positive Intervals: Test a value from the interval $(-1, 1)$ , say $x = 0$ . $(0 - 1)(0 + 1) = (-1)(1) = -1$ , which is negative.Test a value from the interval $(1, \infty)$ , say $x = 2$ . $(2 - 1)(2 + 1) = (1)(3) = 3$ , which is positive.
Combine Positive Intervals: Test a value from the interval $(-1, 1)$ , say $x = 0$ . $(0 - 1)(0 + 1) = (-1)(1) = -1$ , which is negative.Test a value from the interval $(1, \infty)$ , say $x = 2$ . $(2 - 1)(2 + 1) = (1)(3) = 3$ , which is positive.Combine the intervals where the expression is positive. The solution is x < -1 or x > 1.

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2

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\mathrm{knot}=1.15

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1

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\newline

35=15-2 y

\newline

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