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