Solve for x. (x - 3)(x - 6) > 0 Write a compound inequality like 1 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. The number line is divided into three parts: (-∞, 3), (3, 6), and (6, ∞).Test Sign - Interval 1: Test the sign of (x - 3)(x - 6) in the interval (-∞, 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, ∞). 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. The product is positive in the intervals (-∞, 3) and (6, ∞).Write Compound Inequality: Write the solution as a compound inequality. The solution is x 6.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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.

View step-by-step help

Home

Math Problems

Algebra 2

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

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.