Solve for x. x(x - 5) > 0 Write a compound inequality like 1 3. ______

Find Critical Points: Find the critical points of x(x - 5). x(x - 5) = 0 x = 0 or x - 5 = 0 x = 5 Critical points: 0, 5Identify Intervals: Identify the intervals using the critical points. 0 and 5 divide the number line into three parts. Intervals: (-∞, 0), (0, 5), (5, ∞)Check Sign (-∞, 0): Check the sign of x(x - 5) over (-∞, 0). Sign of x: - Sign of (x - 5): - Sign of x(x - 5): (-)(-) = +Check Sign (0, 5): Check the sign of x(x - 5) over (0, 5). Sign of x: + Sign of (x - 5): - Sign of x(x - 5): (+)(-) = -Check Sign (5, ∞): Check the sign of x(x - 5) over (5, ∞). Sign of x: + Sign of (x - 5): + Sign of x(x - 5): (+)(+) = +Positive Intervals: x(x - 5) is positive over (-∞, 0) and (5, ∞). Compound inequality: x 5

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Solve for $x$ . $\newline$ x(x - 5) > 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 - 5) > 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

.______

Find Critical Points: Find the critical points of $x(x - 5)$ . $\newline$ $x(x - 5) = 0$ $\newline$ $x = 0$ or $x - 5 = 0$ $\newline$ $x = 5$ $\newline$ Critical points: $0, 5$
Identify Intervals: Identify the intervals using the critical points. $\newline$ $0$ and $5$ divide the number line into three parts. $\newline$ Intervals: $(-\infty, 0$ ), $(0, 5)$ , $(5, \infty)$
Check Sign $(-\infty, 0)$ : Check the sign of $x(x - 5)$ over $(-\infty, 0)$ . $\newline$ Sign of $x$ : - $\newline$ Sign of $(x - 5)$ : - $\newline$ Sign of $x(x - 5)$ : $(-$ (-) = +)
Check Sign $(0, 5)$ : Check the sign of $x(x - 5)$ over $(0, 5)$ . $\newline$ Sign of $x$ : + $\newline$ Sign of $(x - 5)$ : - $\newline$ Sign of $x(x - 5)$ : $(+)(-) = -$
Check Sign $5, \infty):</b> Check the sign of \$x(x - 5)$ over 5, \infty)\.$\newlineSign of \$x$: +$\newline$Sign of $x - 5$: +$\newline$Sign of $x(x - 5)$: $+(+) = +$
Positive Intervals: $x(x - 5)$ is positive over $(-\infty, 0)$ and $(5, \infty)$.$\newline$Compound inequality: $x < 0$ or $x > 5$

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Solve for xxx.\newlinex(x - 5) > 0\newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 3.______

Solve for $x$ . $\newline$ x(x - 5) > 0 $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.______