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

Find Critical Points: Find the critical points of (x - 1)(x - 2). (x - 1)(x - 2) = 0 x - 1 = 0 implies x = 1. x - 2 = 0 implies x = 2. Critical points: 1, 2Identify Intervals: Identify the intervals using the critical points. 1 and 2 divide the number line into three parts. Intervals: (-∞, 1), (1, 2), (2, ∞)Check Sign (-∞, 1): Check the sign of (x - 1)(x - 2) over (-∞, 1). Sign of (x - 1): - Sign of (x - 2): - Sign of (x - 1)(x - 2): (-)(-) = +Check Sign (1, 2): Check the sign of (x - 1)(x - 2) over (1, 2). Sign of (x - 1): + Sign of (x - 2): - Sign of (x - 1)(x - 2): (+)(-) = -Check Sign (2, ∞): Check the sign of (x - 1)(x - 2) over (2, ∞). Sign of (x - 1): + Sign of (x - 2): + Sign of (x - 1)(x - 2): (+)(+) = +Compound Inequality: (x - 1)(x - 2) ≤ 0 Find the solution as a compound inequality. (x - 1)(x - 2) is non-positive over (1, 2). Compound inequality: 1 ≤ x ≤ 2

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Solve for $x$ . $\newline$ $(x - 1)(x - 2) \leq 0$ $\newline$ 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 - 2) \leq 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

.______

Find Critical Points: Find the critical points of $(x - 1)(x - 2)$ . $(x - 1)(x - 2) = 0$ $x - 1 = 0$ implies $x = 1$ . $x - 2 = 0$ implies $x = 2$ .Critical points: $1, 2$
Identify Intervals: Identify the intervals using the critical points. $\newline$ $1$ and $2$ divide the number line into three parts. $\newline$ Intervals: $(-\infty, 1$ ), $(1, 2)$ , $(2, \infty)$
Check Sign $(-\infty, 1)$ : Check the sign of $(x - 1)(x - 2)$ over $(-\infty, 1)$ . $\newline$ Sign of $(x - 1)$ : - $\newline$ Sign of $(x - 2)$ : - $\newline$ Sign of $(x - 1)(x - 2)$ : $(-$ (-) = +
Check Sign $(1, 2)$ : Check the sign of $(x - 1)(x - 2)$ over $(1, 2)$ . $\newline$ Sign of $(x - 1)$ : + $\newline$ Sign of $(x - 2)$ : - $\newline$ Sign of $(x - 1)(x - 2)$ : $(+)(-) = -$
Check Sign $(2, \infty):$ Check the sign of $(x - 1)(x - 2)$ over $(2, \infty)$ . $\newline$ Sign of $(x - 1)$ : + $\newline$ Sign of $(x - 2)$ : + $\newline$ Sign of $(x - 1)(x - 2)$ : $(+)(+) = +$
Compound Inequality: $x - 1)(x - 2) \leq 0(\newline$ Find the solution as a compound inequality.(\newline\)\$x - 1)(x - 2)\ is non-positive over \$1, 2\).(\newline\)Compound inequality: (1\) \leq x \leq $2$\