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

Find Zeros: Find the zeros of x(x + 2). x(x + 2) = 0 x = 0 or x + 2 = 0 x = 0 or x = -2 Critical points: 0, -2Determine Intervals: Determine the intervals using the critical points. Intervals: (-∞, -2), (-2, 0), (0, ∞)Test Interval (-∞, -2): Test the interval (-∞, -2) to see if x(x + 2) is positive or negative. Choose x = -3: (-3)(-3 + 2) = (-3)(-1) = 3, which is positive.Test Interval (-2, 0): Test the interval (-2, 0) to see if x(x + 2) is positive or negative. Choose x = -1: (-1)(-1 + 2) = (-1)(1) = -1, which is negative.Test Interval (0, ∞): Test the interval (0, ∞) to see if x(x + 2) is positive or negative. Choose x = 1: (1)(1 + 2) = (1)(3) = 3, which is positive.Combine Intervals: Combine the intervals where x(x + 2) is positive or zero. x(x + 2) is greater than or equal to 0 for x in (-∞, -2] and [0, ∞). Compound inequality: x ≤ -2 or x ≥ 0

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

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

Find Zeros: Find the zeros of $x(x + 2)$ . $\newline$ $x(x + 2) = 0$ $\newline$ $x = 0$ or $x + 2 = 0$ $\newline$ $x = 0$ or $x = -2$ $\newline$ Critical points: $0, -2$
Determine Intervals: Determine the intervals using the critical points. $\newline$ Intervals: $(-\infty, -2)$ , $(-2, 0)$ , $(0, \infty)$
Test Interval $(-\infty, -2)$ : Test the interval $(-\infty, -2)$ to see if $x(x + 2)$ is positive or negative. $\newline$ Choose $x = -3$ : $(-3)(-3 + 2) = (-3)(-1) = 3$ , which is positive.
Test Interval $(-2, 0)$ : Test the interval $(-2, 0)$ to see if $x(x + 2)$ is positive or negative. $\newline$ Choose $x = -1$ : $(-1)(-1 + 2) = (-1)(1) = -1$ , which is negative.
Test Interval $0, \infty):</b> Test the interval \$0, \infty) to see if \$x(x + 2)$ is positive or negative. $\newline$ Choose $x = 1$ : $1)(1 + 2) = (1)(3) = 3$ , which is positive.
Combine Intervals: Combine the intervals where $x(x + 2)$ is positive or zero. $\newline$ $x(x + 2)$ is greater than or equal to $0$ for $x$ in $(-\infty, -2]$ and $[0, \infty)$ . $\newline$ Compound inequality: $x \leq -2$ or $x \geq 0$

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Solve for xxx.\newlinex(x+2)≥0x(x + 2) \geq 0x(x+2)≥0\newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 3.

Solve for $x$ . $\newline$ $x(x + 2) \geq 0$ $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.