Solve for x. x(x + 6) 3. ______

Find Zeros and Critical Points: Find the zeros of x(x + 6). x = 0 or x + 6 = 0 x = 0 or x = -6 Critical points: 0, -6Determine Intervals: Determine the intervals using the critical points. Intervals: (-∞, -6), (-6, 0), (0, ∞)Test Interval (-∞, -6): Test the interval (-∞, -6) to see if x(x + 6) is negative or positive. Pick x = -7: (-7)(-7 + 6) = (-7)(-1) = 7, which is positive.Test Interval (-6, 0): Test the interval (-6, 0) to see if x(x + 6) is negative or positive. Pick x = -3: (-3)(-3 + 6) = (-3)(3) = -9, which is negative.Test Interval (0, ∞): Test the interval (0, ∞) to see if x(x + 6) is negative or positive. Pick x = 1: (1)(1 + 6) = (1)(7) = 7, which is positive.Identify Negative Intervals: Since we want x(x + 6) < 0, we look for intervals where the product is negative. The interval (-6, 0) is where x(x + 6) is negative. Compound inequality: -6 < x < 0

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

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Algebra 2

Solve quadratic inequalities

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Q. Solve for

x

\newline

x(x + 6) < 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

.______

Find Zeros and Critical Points: Find the zeros of $x(x + 6)$ .
$x = 0$ or $x + 6 = 0$
$x = 0$ or $x = -6$
Critical points: $0, -6$
Determine Intervals: Determine the intervals using the critical points. $\newline$ Intervals: $(-\infty, -6)$ , $(-6, 0)$ , $(0, \infty)$
Test Interval $(-\infty, -6)$ : Test the interval $(-\infty, -6)$ to see if $x(x + 6)$ is negative or positive. $\newline$ Pick $x = -7$ : $(-7)(-7 + 6) = (-7)(-1) = 7$ , which is positive.
Test Interval $(-6, 0)$ : Test the interval $(-6, 0)$ to see if $x(x + 6)$ is negative or positive. $\newline$ Pick $x = -3$ : $(-3)(-3 + 6) = (-3)(3) = -9$ , which is negative.
Test Interval $0, \infty):</b> Test the interval \$0, \infty) to see if \$x(x + 6)$ is negative or positive. $\newline$ Pick $x = 1$ : $1)(1 + 6) = (1)(7) = 7$ , which is positive.
Identify Negative Intervals: Since we want x(x + 6) < 0, we look for intervals where the product is negative. $\newline$ The interval $(-6, 0)$ is where $x(x + 6)$ is negative. $\newline$ Compound inequality: -6 < x < 0

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Solve for xxx.\newlinex(x + 6) < 0\newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 3.______

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