Solve for $x$ . $\newline$ $(x - 5)(x - 6) > 0$ $\newline$ 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 - 5)(x - 6) > 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

Divide Intervals: Divide the number line into intervals using the critical points. $\newline$ Intervals: $(-\infty, 5)$ , $(5, 6)$ , $(6, \infty)$ .
Test Interval $(-\infty, 5)$ : Test the interval $(-\infty, 5)$ to determine the sign of $(x - 5)(x - 6)$ . Let $x = 4$ , then $(4 - 5)(4 - 6) = (-1)(-2) = 2$ , which is positive.
Test Interval $(5, 6)$ : Test the interval $(5, 6)$ to determine the sign of $(x - 5)(x - 6)$ . Let $x = 5.5$ , then $(5.5 - 5)(5.5 - 6) = (0.5)(-0.5) = -0.25$ , which is negative.
Test Interval $6, \infty):</b> Test the interval \$6, \infty) to determine the sign of \$x - 5)(x - 6). Let \$x = 7$ , then $7 - 5)(7 - 6) = (2)(1) = 2$ , which is positive.
Final Solution: Since we want $(x - 5)(x - 6) > 0$ , we take the intervals where the expression is positive. $\newline$ The solution is $x < 5$ or $x > 6$ .

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Solve for xxx.\newline(x−5)(x−6)>0(x - 5)(x - 6) > 0(x−5)(x−6)>0\newline Write a compound inequality like 1<x<31 < x < 31<x<3 or like x<1x < 1x<1 or x>3x > 3x>3.

Solve for $x$ . $\newline$ $(x - 5)(x - 6) > 0$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ .