Solve for x. x(x + 2) ≤ 0 Write a compound inequality like 1 3. ______

Find Critical Points: Find the critical points of x(x + 2). x(x + 2) = 0 x = 0 or x + 2 = 0 x = 0 or x = -2 Critical points: 0, -2Identify Intervals: Identify the intervals using the critical points. -2 and 0 divide the number line into three parts. Intervals: (-∞, -2), (-2, 0), (0, ∞)Sign Analysis (-∞, -2): Determine the sign of x(x + 2) over (-∞, -2). Sign of x: - Sign of (x + 2): - Sign of x(x + 2): (-)(-) = +Sign Analysis (-2, 0): Determine the sign of x(x + 2) over (-2, 0). Sign of x: - Sign of (x + 2): + Sign of x(x + 2): (-)(+) = -Sign Analysis (0, ∞): Determine the sign of x(x + 2) over (0, ∞). Sign of x: + Sign of (x + 2): + Sign of x(x + 2): (+)(+) = +Non-Positive Range: x(x + 2) is non-positive over (-2, 0). Compound inequality: -2 ≤ x ≤ 0

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Solve for $x$ . $\newline$ $x(x + 2) \leq 0$ $\newline$ 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 + 2) \leq 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

.______

Find Critical Points: Find the critical points of $x(x + 2)$ . $\newline$ $x(x + 2) = 0$ $\newline$ $x = 0 \text{ or } x + 2 = 0$ $\newline$ $x = 0 \text{ or } x = -2$ $\newline$ Critical points: $0, -2$
Identify Intervals: Identify the intervals using the critical points. $\newline$ $-2$ and $0$ divide the number line into three parts. $\newline$ Intervals: (-$\newline∞, -2), (-2, 0), (0, ∞)$
Sign Analysis $(-\infty, -2)$ : Determine the sign of $x(x + 2)$ over $(-\infty, -2)$ . $\newline$ Sign of $x$ : - $\newline$ Sign of $(x + 2)$ : - $\newline$ Sign of $x(x + 2)$ : $(-$ (-) = +\)
Sign Analysis $(-2, 0)$ : Determine the sign of $x(x + 2)$ over $(-2, 0)$ . $\newline$ Sign of $x$ : - $\newline$ Sign of $(x + 2)$ : + $\newline$ Sign of $x(x + 2)$ : $(-$ (+) = -)
Sign Analysis $(0, \infty):$ Determine the sign of $x(x + 2)$ over $(0, \infty)$ . $\newline$ Sign of $x$ : + $\newline$ Sign of $(x + 2)$ : + $\newline$ Sign of $x(x + 2)$ : $(+)(+) = +$
Non-Positive Range: $x(x + 2)$ is non-positive over $(-2, 0)$ . $\newline$ Compound inequality: $-2 \leq x \leq 0$