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

Find Critical Points: Find the critical points of (x + 2)(x + 3). (x + 2)(x + 3) = 0 x + 2 = 0 implies x = -2. x + 3 = 0 implies x = -3. Critical points: -2, -3Identify Intervals: Identify the intervals using the critical points. -3 and -2 divide the number line into three parts. Intervals: (-∞, -3), (-3, -2), (-2, ∞)Check Sign (-∞, -3): Check the sign of (x + 2)(x + 3) over (-∞, -3). Sign of (x + 2): - Sign of (x + 3): - Sign of (x + 2)(x + 3): (-)(-) = +Check Sign (-3, -2): Check the sign of (x + 2)(x + 3) over (-3, -2). Sign of (x + 2): - Sign of (x + 3): + Sign of (x + 2)(x + 3): (-)(+) = -Check Sign (-2, ∞): Check the sign of (x + 2)(x + 3) over (-2, ∞). Sign of (x + 2): + Sign of (x + 3): + Sign of (x + 2)(x + 3): (+)(+) = +Compound Inequality: (x + 2)(x + 3) is greater than or equal to 0 over (-∞, -3) or (-2, ∞). Compound inequality: x ≤ -3 or x ≥ -2

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Solve for $x$ . $\newline$ $(x + 2)(x + 3) \geq 0$ $\newline$ 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 + 2)(x + 3) \geq 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

Find Critical Points: Find the critical points of $(x + 2)(x + 3)$ . $(x + 2)(x + 3) = 0$ $x + 2 = 0$ implies $x = -2$ . $x + 3 = 0$ implies $x = -3$ .Critical points: $-2, -3$
Identify Intervals: Identify the intervals using the critical points. $\newline$ $-3$ and $-2$ divide the number line into three parts. $\newline$ Intervals: (-$\newline∞, -3), (-3, -2), (-2, ∞)$
Check Sign $(-\infty, -3)$ : Check the sign of $(x + 2)(x + 3)$ over $(-\infty, -3)$ . $\newline$ Sign of $(x + 2)$ : - $\newline$ Sign of $(x + 3)$ : - $\newline$ Sign of $(x + 2)(x + 3)$ : $(-$ (-) = +
Check Sign $(-3, -2)$ : Check the sign of $(x + 2)(x + 3)$ over $(-3, -2)$ . $\newline$ Sign of $(x + 2)$ : - $\newline$ Sign of $(x + 3)$ : + $\newline$ Sign of $(x + 2)(x + 3)$ : $(-$ (+) = -
Check Sign $(-2, \infty):$ Check the sign of $(x + 2)(x + 3)$ over $(-2, \infty).$ $\newline$ Sign of $(x + 2): +$ $\newline$ Sign of $(x + 3): +$ $\newline$ Sign of (x + \(2)(x + $3$ ): (+)(+) = +\
Compound Inequality: $(x + 2)(x + 3)$ is greater than or equal to $0$ over $(-\infty, -3)$ or $(-2, \infty)$ . $\newline$ Compound inequality: $x \leq -3$ or $x \geq -2$