Solve for $x$ . $\newline$ $x(x + 4) > 0$ $\newline$ 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(x + 4) > 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

Find Critical Points: Find the critical points of $x(x + 4)$ . $\newline$ $x(x + 4) = 0$ $\newline$ $x = 0 \text{ or } x + 4 = 0$ $\newline$ $x = -4$ $\newline$ Critical points: $0, -4$
Identify Intervals: Identify the intervals using the critical points. $\newline$ $-4$ and $0$ divide the number line into three parts. $\newline$ Intervals: $(-\infty, -4$ ), $(-4, 0$ ), $(0, \infty)$
Check Sign $(-\infty, -4)$ : Check the sign of $x(x + 4)$ over $(-\infty, -4)$ . $\newline$ Sign of $x$ : - $\newline$ Sign of $(x + 4)$ : - $\newline$ Sign of $x(x + 4)$ : $(-$ (-) = +\)
Check Sign $(-4, 0)$ : Check the sign of $x(x + 4)$ over $(-4, 0)$ . $\newline$ Sign of $x$ : - $\newline$ Sign of $x + 4$ : + $\newline$ Sign of $x(x + 4)$ : $(-)(+) = -$
Check Sign $0, \infty):</b> Check the sign of \$x(x + 4)$ over $0, \infty$ . $\newline$ Sign of $x$ : + $\newline$ Sign of $x + 4$ : + $\newline$ Sign of $x(x + 4)$ : $+(+) = +$
Positive Intervals: $x(x + 4)$ is positive over $(-\infty, -4)$ and $(0, \infty)$ . $\newline$ Compound inequality: $x < -4$ or $x > 0$

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Solve for xxx.\newlinex(x+4)>0x(x + 4) > 0x(x+4)>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 $x$ . $\newline$ $x(x + 4) > 0$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ .