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. 0 and 2 divide the number line into three parts. Intervals: (-∞, 0), (0, 2), (2, ∞)Determine Sign: Determine the sign of x(x - 2) over (-∞, 0). Sign of x: - Sign of (x - 2): - Sign of x(x - 2): (-)(-) = +Determine Sign: Determine the sign of x(x - 2) over (0, 2). Sign of x: + Sign of (x - 2): - Sign of x(x - 2): (+)(-) = -Determine Sign: Determine the sign of x(x - 2) over (2, ∞). Sign of x: + Sign of (x - 2): + Sign of x(x - 2): (+)(+) = +Determine Inequality: x(x - 2) is greater than or equal to 0 over (-∞, 0] and [2, ∞). Compound inequality: x ≤ 0 or x ≥ 2

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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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Math Problems

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 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. $\newline$ $0$ and $2$ divide the number line into three parts. $\newline$ Intervals: $(-\infty, 0$ ), $(0, 2)$ , $(2, \infty)$
Determine Sign: Determine the sign of $x(x - 2)$ over $(-\infty, 0)$ . $\newline$ Sign of $x$ : $-$ $\newline$ Sign of $(x - 2)$ : $-$ $\newline$ Sign of $x(x - 2)$ : $(-)(-) = +$
Determine Sign: Determine the sign of $x(x - 2)$ over $(0, 2)$ . $\newline$ Sign of $x$ : $+$ $\newline$ Sign of $(x - 2)$ : $-$ $\newline$ Sign of $x(x - 2)$ : $(+)(-) = -$
Determine Sign: Determine the sign of $x(x - 2)$ over $(2, \infty)$ . $\newline$ Sign of $x$ : + $\newline$ Sign of $(x - 2)$ : + $\newline$ Sign of $x(x - 2)$ : $(+)(+)$ = +
Determine Inequality: $x(x - 2)$ is greater than or equal to $0$ over $(-\infty, 0]$ and $[2, \infty)$ . $\newline$ Compound inequality: $x \leq 0$ or $x \geq 2$