Solve for x. (x - 5)(x - 6) > 0 Write a compound inequality like 1 3. ______

Divide Intervals: Divide the number line into intervals using the critical points. Intervals: (-∞, 5), (5, 6), (6, ∞).Test Interval (-∞, 5): Test the interval (-∞, 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, ∞): Test the interval (6, ∞) 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. The solution is x 6.

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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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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\newline Write a compound inequality like 1 < x < 3 or like x < 1 or x > 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.