Solve for $x$ . $\newline$ $x(x + 2) \geq 0$ $\newline$ 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(x + 2) \geq 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

Find Zeros: Find the zeros of $x(x + 2)$ . $\newline$ $x(x + 2) = 0$ $\newline$ $x = 0$ or $x + 2 = 0$ $\newline$ $x = 0$ or $x = -2$ $\newline$ Critical points: $0, -2$
Determine Intervals: Determine the intervals using the critical points. $\newline$ Intervals: $(-\infty, -2)$ , $(-2, 0)$ , $(0, \infty)$
Test Interval $(-\infty, -2)$ : Test the interval $(-\infty, -2)$ to see if $x(x + 2)$ is positive or negative. $\newline$ Choose $x = -3$ : $(-3)(-3 + 2) = (-3)(-1) = 3$ , which is positive.
Test Interval $(-2, 0)$ : Test the interval $(-2, 0)$ to see if $x(x + 2)$ is positive or negative. $\newline$ Choose $x = -1$ : $(-1)(-1 + 2) = (-1)(1) = -1$ , which is negative.
Test Interval $0, \infty):</b> Test the interval \$0, \infty) to see if \$x(x + 2)$ is positive or negative. $\newline$ Choose $x = 1$ : $1)(1 + 2) = (1)(3) = 3$ , which is positive.
Combine Intervals: Combine the intervals where $x(x + 2)$ is positive or zero. $\newline$ $x(x + 2)$ is greater than or equal to $0$ for $x$ in $(-\infty, -2]$ and $[0, \infty)$ . $\newline$ Compound inequality: $x \leq -2$ or $x \geq 0$

More problems from Solve quadratic inequalities

Question
Solve for $s$ . $\newline$ $|s| + 3 \geq 8$ $\newline$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ . Use integers, proper fractions, or improper fractions in simplest form. $\newline$ $\newline$ ______
Get tutor help
Posted 2 months ago

Question
Solve for $x$ . $\newline$ $(x - 1)(x + 1) > 0$ $\newline$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ . $\newline$ ______
Get tutor help
Posted 2 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 2 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 4 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 4 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 2 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 1 month 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 4 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 3 months ago

View all (169)

Solve for xxx.\newlinex(x+2)≥0x(x + 2) \geq 0x(x+2)≥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 $x$ . $\newline$ $x(x + 2) \geq 0$ $\newline$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ .