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

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

.______

Plot Zeros and Test Intervals: Plot the zeros on a number line and test the intervals. The intervals are $(-\infty, 5)$ , $(5, 6)$ , and $(6, \infty)$ .
Test Interval $(-\infty, 5):$ Test the interval $(-\infty, 5)$ by picking a number less than $5$ , say $x = 4$ . $(4 - 5)(4 - 6) = (-1)(-2) = 2$ , which is positive.
Test Interval $5, 6)\:</b> Test the interval \$5, 6)\ by picking a number between \$5$ and $6$ , say $x = 5.5$ . $\$5.5 - 5$ $5.5 - 6$ = $0.5$ $-0.5$ = $-0$ . $25$ \), which is negative.
Test Interval $6, \infty):</b> Test the interval \$6, \infty) by picking a number greater than \$6$ , say $x = 7$ . $(7 - 5)(7 - 6) = (2)(1) = 2$ , which is positive.
Combine Positive Intervals: Combine the intervals where the product is positive or zero. $\newline$ The solution is $x \leq 5$ or $x \geq 6$ .

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