Solve for x. x(x - 4) 3. ______

Find Zeros: Find the zeros of x(x - 4). x = 0 or x - 4 = 0 x = 0 or x = 4 Critical points: 0, 4Determine Intervals: Determine the intervals using the critical points. Intervals: (-∞, 0), (0, 4), (4, ∞)Test Interval (-∞, 0): Test the interval (-∞, 0) by picking a number, say -1. (-1)(-1 - 4) = (-1)(-5) = 5, which is > 0.Test Interval (0, 4): Test the interval (0, 4) by picking a number, say 2. (2)(2 - 4) = (2)(-2) = -4, which is 0.Combine Intervals: Combine the intervals where the product is less than 0. The solution is the interval (0, 4). Compound inequality: 0 < x < 4

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Solve for $x$ . $\newline$ x(x - 4) < 0 $\newline$ $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. $\newline$ ______ $\newline$

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Algebra 2

Solve quadratic inequalities

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Q. Solve for

x

\newline

x(x - 4) < 0

\newline

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

\newline

______

\newline

Find Zeros: Find the zeros of $x(x - 4)$ . $\newline$ $x = 0$ or $x - 4 = 0$ $\newline$ $x = 0$ or $x = 4$ $\newline$ Critical points: $0, 4$
Determine Intervals: Determine the intervals using the critical points. $\newline$ Intervals: $(-\infty, 0)$ , $(0, 4)$ , $(4, \infty)$
Test Interval $(-\infty, 0)$ : Test the interval $(-\infty, 0)$ by picking a number, say $-1$ . $(-1)(-1 - 4) = (-1)(-5) = 5,$ which is \ (> $0$ )\.
Test Interval $(0, 4)$ : Test the interval $(0, 4)$ by picking a number, say $2$ . $(2)(2 - 4) = (2)(-2) = -4$ , which is < 0.
Test Interval $4, \infty):</b> Test the interval \$4, \infty) by picking a number, say \$5$ . $(5)(5 - 4) = (5)(1) = 5$ , which is < 0.
Combine Intervals: Combine the intervals where the product is less than $0$ . The solution is the interval $(0, 4)$ . Compound inequality: 0 < x < 4

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Solve for xxx.\newlinex(x - 4) < 0\newline\newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 3.\newline______\newline

Solve for $x$ . $\newline$ x(x - 4) < 0 $\newline$ $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. $\newline$ ______ $\newline$