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Solve for $x$ . $\newline$ $x(x + 4) \leq 0$ $\newline$ 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(x + 4) \leq 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

or

x > 3

.______

Find Zeros: Find the zeros of the quadratic equation $x(x + 4) = 0$ . $\newline$ $x = 0$ or $x + 4 = 0$ $\newline$ $x = 0$ or $x = -4$
Determine Intervals: Determine the intervals to test based on the zeros. $\newline$ Intervals: $(-\infty, -4)$ , $(-4, 0)$ , $(0, \infty)$
Test Interval $-\infty$ to $-4$ : Test the interval $(-\infty, -4)$ by picking a point, say $x = -5$ . $(-5)(-5 + 4) = (-5)(-1) = 5$ , which is > 0.
Test Interval $-4$ to $0$ : Test the interval $(-4, 0)$ by picking a point, say $x = -2$ . $(-2)(-2 + 4) = (-2)(2) = -4$ , which is < 0.
Test Interval $0$ to $\infty$ : Test the interval $(0, \infty)$ by picking a point, say $x = 1$ . $\newline$ $(1)(1 + 4) = (1)(5) = 5$ , which is > 0.
Combine Intervals: Combine the intervals where the product $x(x + 4)$ is $\leq 0$ . The product is non-positive in the interval $(-4, 0]$ .

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

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Question

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\newline

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

\newline

1

\newline

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Question

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p

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\newline

1

\newline

0.018 p-100=4580

\newline

0.018 p+100=4580

\newline

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\newline

(100+0.018) p=4580

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Question

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1

500

2

500

-mile journey is traveling at

450

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150

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\newline

1

\mathrm{knot}=1.15

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1

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\newline

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Question

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y

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24

inches per year. Which of the following equations best describes this situation?

\newline

1

=12

\newline

1

\newline

35=15+2 y

\newline

35=15+24 y

\newline

35=15-2 y

\newline

35=15-24 y

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Question

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\newline

1

\newline

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\newline

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