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

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

.______

Find Zeros: Find the zeros of the quadratic expression. $\newline$ $(x - 1) = 0$ gives $x = 1$ . $\newline$ $(x - 2) = 0$ gives $x = 2$ . $\newline$ Critical points: $1$ , $2$ .
Determine Intervals: Determine the intervals to test around the critical points. $\newline$ Intervals: $(-\infty, 1)$ , $(1, 2)$ , $(2, \infty)$ .
Test Interval $(-\infty, 1):$ Test the interval $(-\infty, 1)$ by picking a number less than $1$ , say $x = 0$ . $(0 - 1)(0 - 2) = (1)(2) = 2$ , which is $> 0$ .
Test Interval $1, 2)\:</b> Test the interval \$1, 2)\ by picking a number between \$1$ and $2$ , say $x = 1.5$ . $(1.5 - 1)(1.5 - 2) = (0.5)(-0.5) = -0.25$ , which is $< 0$ .
Test Interval $2, \infty):</b> Test the interval \$2, \infty) by picking a number greater than \$2$ , say $x = 3$ . $(3 - 1)(3 - 2) = (2)(1) = 2$ , which is $< 0$ .
Combine Intervals: Combine the intervals where the product is less than $0$ . The product is less than $0$ in the interval $(1, 2)$ . Compound inequality: $1 < x < 2$ .

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Solve for xxx.\newline(x−1)(x−2)<0 (x - 1)(x - 2) < 0 (x−1)(x−2)<0\newlineWrite a compound inequality like 1<x<31 < x < 31<x<3 or like x<1x < 1x<1 or x>3x > 3x>3.______

Solve for $x$ . $\newline$ $(x - 1)(x - 2) < 0$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ .______