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.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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.

View step-by-step help

Home

Math Problems

Algebra 2

Solve quadratic inequalities

Full solution

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.

More problems from Solve quadratic inequalities

Question
Solve for $s$ . $\newline$ $|s| + 3 \geq 8$
Get tutor help
Posted 4 months ago

Question
Which compound inequality represents the value of $x ?$ $\newline$ $(x - 1)(x + 1) > 0$ $\newline$
Get tutor help
Posted 4 months ago

Question
A particular company charges advertisers a one time cost of $\$500$ , in addition to $\$4.50$ for every one thousand times an advertisement is shown on the company's webpage. An advertiser wants its ad to appear $M$ thousand times on the webpage, but does not want to spend more than $\$5,000$ . Which of the following inequalities best describes the situation? $\newline$ Choices: $\newline$ (A) $500+4.50M\geq5,000$ $\newline$ (B) $4.50+500M>5,000$ $\newline$ (C) $500+4.50M\leq5,000$ $\newline$ (D) $500+4.50M<5,000$
Get tutor help
Posted 7 months ago

Question
$7x+1 < x+9$ $\newline$ Which of the following best describes the solutions to the inequality shown? $\newline$ Choose $1$ answer: $\newline$ (A) $x > \frac{4}{3}$ $\newline$ (B) $x < \frac{4}{3}$ $\newline$ (C) $x < 1$ $\newline$ (D) $x < \frac{5}{3}$
Get tutor help
Posted 4 months ago

Question
$52-3x < -14$ $\newline$ Which of the following best describes the solutions to the inequality shown? $\newline$ Choose $1$ answer: $\newline$ (A) $x > -\frac{38}{3}$ $\newline$ (B) $x > \frac{38}{3}$ $\newline$ (C) $x < 22$ $\newline$ (D) $x > 22$
Get tutor help
Posted 10 months ago

Question
$5-3x > 2x+2$ $\newline$ Which of the following best describes the solutions to the inequality shown? $\newline$ Choose $1$ answer: $\newline$ (A) $x < \frac{7}{5}$ $\newline$ (B) $x < 3$ $\newline$ (C) $x < \frac{3}{5}$ $\newline$ (D) $x > \frac{3}{5}$
Get tutor help
Posted 10 months ago

Question
Rani is a real estate agent. For each house she sells, she pays $\$ 100$ in fees, but earns a commission of $1.8 \%$ of the selling price of the house. Rani's total profit from a particular house is $\$ 4,580$ . If $p$ represents the selling price of the house, which equation best models the situation? $\newline$ Choose $1$ answer: $\newline$ (A) $0.018 p-100=4580$ $\newline$ (B) $0.018 p+100=4580$ $\newline$ (C) $(100-0.018) p=4580$ $\newline$ (D) $(100+0.018) p=4580$
Get tutor help
Posted 8 months ago

Question
A commercial airplane that is $1$ , $500$ miles into a $2$ , $500$ -mile journey is traveling at $450$ knots in still air when it picks up a tailwind of $150$ knots (in the same direction). If $h$ is the number of hours remaining in the airplane's flight, which of the following equations best describes the situation? $\newline$ $1$ $\mathrm{knot}=1.15$ miles per hour (mph) $\newline$ Choose $1$ answer: $\newline$ (A) $1,500+690 h=2,500$ $\newline$ (B) $1,500+600 h=2,500$ $\newline$ (C) $1,500-600 h=2,500$ $\newline$ (D) $1,500-690 h=2,500$
Get tutor help
Posted 7 months ago

Question
A weeping willow that is $15$ feet in height grows to a maximum height of $35$ feet in $y$ years at a constant rate of $24$ inches per year. Which of the following equations best describes this situation? $\newline$ $1$ foot $=12$ inches $\newline$ Choose $1$ answer: $\newline$ (A) $35=15+2 y$ $\newline$ (B) $35=15+24 y$ $\newline$ (C) $35=15-2 y$ $\newline$ (D) $35=15-24 y$
Get tutor help
Posted 10 months ago

Question
The gas mileage for a car is $23$ miles per gallon when the car travels at $60$ miles per hour. The car begins a trip with $13$ gallons in its tank, travels at an average speed of $60$ miles per hour for $h$ hours, and ends the trip with $10$ gallons in its tank. Which of the following equations best models this situation? $\newline$ Choose $1$ answer: $\newline$ (A) $13-\frac{23 h}{60}=10$ $\newline$ (B) $13-\frac{60 h}{23}=10$ $\newline$ (C) $\frac{13-60 h}{23}=10$ $\newline$ (D) $\frac{13-23 h}{60}=10$
Get tutor help
Posted 8 months ago

View all (126)

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.