Solve for x. (x - 1)(x - 4) ≥ 0 Write a compound inequality like 1 3. ______

Find Critical Points: Find the critical points of (x - 1)(x - 4). (x - 1)(x - 4) = 0 x - 1 = 0 implies x = 1. x - 4 = 0 implies x = 4. Critical points: 1, 4Identify Intervals: Identify the intervals using the critical points. 1 and 4 divide the number line into three parts. Intervals: (-∞, 1), (1, 4), (4, ∞)Check Sign (-∞, 1): Check the sign of (x - 1)(x - 4) over (-∞, 1). Sign of (x - 1): - Sign of (x - 4): - Sign of (x - 1)(x - 4): (-)(-) = +Check Sign (1, 4): Check the sign of (x - 1)(x - 4) over (1, 4). Sign of (x - 1): + Sign of (x - 4): - Sign of (x - 1)(x - 4): (+)(-) = -Check Sign (4, ∞): Check the sign of (x - 1)(x - 4) over (4, ∞). Sign of (x - 1): + Sign of (x - 4): + Sign of (x - 1)(x - 4): (+)(+) = +Compound Inequality: (x - 1)(x - 4) ≥ 0 Find the solution as a compound inequality. (x - 1)(x - 4) is non-negative over (-∞, 1] and [4, ∞). Compound inequality: x ≤ 1 or x ≥ 4

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Solve for $x$ . $\newline$ $(x - 1)(x - 4) \geq 0$ $\newline$ 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 - 1)(x - 4) \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 $(x - 1)(x - 4)$ . $(x - 1)(x - 4) = 0$ $x - 1 = 0$ implies $x = 1$ . $x - 4 = 0$ implies $x = 4$ .Critical points: $1$ , $4$
Identify Intervals: Identify the intervals using the critical points. $\newline$ $1$ and $4$ divide the number line into three parts. $\newline$ Intervals: $(-\infty, 1$ ), $(1, 4)$ , $(4, \infty)$
Check Sign $(-\infty, 1)$ : Check the sign of $(x - 1)(x - 4)$ over $(-\infty, 1)$ . $\newline$ Sign of $(x - 1)$ : - $\newline$ Sign of $(x - 4)$ : - $\newline$ Sign of $(x - 1)(x - 4)$ : $(-$ (-) = +
Check Sign $(1, 4)$ : Check the sign of $(x - 1)(x - 4)$ over $(1, 4)$ . $\newline$ Sign of $(x - 1)$ : + $\newline$ Sign of $(x - 4)$ : - $\newline$ Sign of $(x - 1)(x - 4)$ : $(+)(-) = -$
Check Sign $(4, \infty):$ Check the sign of $(x - 1)(x - 4)$ over $(4, \infty)$ . $\newline$ Sign of $(x - 1)$ : + $\newline$ Sign of $(x - 4)$ : + $\newline$ Sign of $(x - 1)(x - 4)$ : $(+)(+) = +$
Compound Inequality: $(x - 1)(x - 4) \geq 0$ $\newline$ Find the solution as a compound inequality. $\newline$ $(x - 1)(x - 4)$ is non-negative over $(-\infty, 1]$ and $[4, \infty)$ . $\newline$ Compound inequality: $x \leq 1$ or $x \geq 4$