Solve for x. x(x + 4) > 0 Write a compound inequality like 1 3. ______

Find Critical Points: Find the critical points of x(x + 4). x(x + 4) = 0 x = 0 or x + 4 = 0 x = -4 Critical points: 0, -4Identify Intervals: Identify the intervals using the critical points. -4 and 0 divide the number line into three parts. Intervals: (-∞, -4), (-4, 0), (0, ∞)Check Sign (-∞, -4): Check the sign of x(x + 4) over (-∞, -4). Sign of x: - Sign of (x + 4): - Sign of x(x + 4): (-)(-) = +Check Sign (-4, 0): Check the sign of x(x + 4) over (-4, 0). Sign of x: - Sign of (x + 4): + Sign of x(x + 4): (-)(+) = -Check Sign (0, ∞): Check the sign of x(x + 4) over (0, ∞). Sign of x: + Sign of (x + 4): + Sign of x(x + 4): (+)(+) = +Positive Intervals: x(x + 4) is positive over (-∞, -4) and (0, ∞). Compound inequality: x 0

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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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Algebra 2

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) > 0\newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 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.