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

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Solve quadratic inequalities

Full solution

Q. Solve for

x

.

\newline

(x - 3)(x - 6) > 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

or

x > 3

.

Find Zeros: Find the zeros of the equation $(x - 3)(x - 6) = 0$ . $x - 3 = 0$ gives $x = 3$ . $x - 6 = 0$ gives $x = 6$ .Critical points: $3, 6$ .
Determine Intervals: Determine the intervals using the critical points. $\newline$ The number line is divided into three parts: $(-\infty, 3)$ , $(3, 6)$ , and $(6, \infty)$ .
Test Sign - Interval $1$ : Test the sign of $(x - 3)(x - 6)$ in the interval $(-\infty, 3)$ . Choose a test point, like $x = 0$ . $(0 - 3)(0 - 6) = (+)(+)$ which is positive.
Test Sign - Interval $2$ : Test the sign of $(x - 3)(x - 6)$ in the interval $(3, 6)$ . Choose a test point, like $x = 4$ . $(4 - 3)(4 - 6) = (+)(-)$ which is negative.
Test Sign - Interval $3$ : Test the sign of $(x - 3)(x - 6)$ in the interval $(6, \infty)$ . Choose a test point, like $x = 7$ . $(7 - 3)(7 - 6) = (+)(+)$ which is positive.
Identify Positive Intervals: Since we want $(x - 3)(x - 6) > 0$ , we look for intervals where the product is positive. $\newline$ The product is positive in the intervals $(-\infty, 3)$ and $(6, \infty)$ .
Write Compound Inequality: Write the solution as a compound inequality. $\newline$ The solution is $x < 3$ or $x > 6$ .

More problems from Solve quadratic inequalities

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Which of the following best describes the solutions to the inequality shown?

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0.018 p-100=4580

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1

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1

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1

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\newline

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\newline

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\newline

1

\newline

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