Solve for x. (x - 1)(x + 1) > 0 Write a compound inequality like 1 3. ______

Find Zeros: Find the zeros of the quadratic by setting each factor to zero. x - 1 = 0 gives x = 1. x + 1 = 0 gives x = -1.Determine Intervals: Determine the intervals to test around the zeros: (-∞, -1), (-1, 1), and (1, ∞).Test Around Zeros: Test a value from the interval (-∞, -1), say x = -2. (-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.Test a value from the interval (1, ∞), 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.

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Solve for $x$ . $\newline$ (x - 1)(x + 1) > 0 $\newline$ $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. $\newline$ ______ $\newline$

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Math Problems

Algebra 2

Solve quadratic inequalities

Full solution

Q. Solve for

x

\newline

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

\newline

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

\newline

______

\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.