Solve for $x$ . $\newline$ $(x - 6)(x + 6) < 0$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ .

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Solve quadratic inequalities

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Q. Solve for

x

\newline

(x - 6)(x + 6) < 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

Plot Zeros and Test Intervals: Plot the zeros on a number line and test the intervals. The intervals are $(-\infty, -6)$ , $(-6, 6)$ , and $(6, \infty)$ .
Test Interval $(-\infty, -6)$ : Test the interval $(-\infty, -6)$ by picking a number less than $-6$ , say $-7$ . $(-7 - 6)(-7 + 6) = (-13)(-1) = 13$ , which is positive.
Test Interval $(-6, 6)$ : Test the interval $(-6, 6)$ by picking a number between $-6$ and $6$ , say $0$ . $(0 - 6)(0 + 6) = (-6)(6) = -36$ , which is negative.
Test Interval $6, \infty):</b> Test the interval \$6, \infty) by picking a number greater than \$6$ , say $7$ . $(7 - 6)(7 + 6) = (1)(13) = 13$ , which is positive.
Identify Negative Product Interval: Since we want $(x - 6)(x + 6) < 0$ , the solution is the interval where the product is negative. $\newline$ The product is negative in the interval $(-6, 6)$ .
Write Compound Inequality: Write the solution as a compound inequality. $-6 < x < 6$ .

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Solve for xxx.\newline(x−6)(x+6)<0 (x - 6)(x + 6) < 0 (x−6)(x+6)<0\newlineWrite a compound inequality like 1<x<31 < x < 31<x<3 or like x<1x < 1x<1 or x>3x > 3x>3.

Solve for $x$ . $\newline$ $(x - 6)(x + 6) < 0$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ .