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Solve for $x$ . $\newline$ $(x - 1)(x - 4) \geq 0$ $\newline$ 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 - 1)(x - 4) \geq 0

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

or

x > 3

.

Find Critical Points: Find the critical points of $(x - 1)(x - 4)$ . $(x - 1)(x - 4) = 0$ $x - 1 = 0$ implies $x = 1$ . $x - 4 = 0$ implies $x = 4$ .Critical points: $1$ , $4$
Identify Intervals: Identify the intervals using the critical points. $\newline$ $1$ and $4$ divide the number line into three parts. $\newline$ Intervals: $(-\infty, 1$ ), $(1, 4)$ , $(4, \infty)$
Check Sign $(-\infty, 1)$ : Check the sign of $(x - 1)(x - 4)$ over $(-\infty, 1)$ . $\newline$ Sign of $(x - 1)$ : - $\newline$ Sign of $(x - 4)$ : - $\newline$ Sign of $(x - 1)(x - 4)$ : $(-$ (-) = +
Check Sign $(1, 4)$ : Check the sign of $(x - 1)(x - 4)$ over $(1, 4)$ . $\newline$ Sign of $(x - 1)$ : + $\newline$ Sign of $(x - 4)$ : - $\newline$ Sign of $(x - 1)(x - 4)$ : $(+)(-) = -$
Check Sign $(4, \infty):$ Check the sign of $(x - 1)(x - 4)$ over $(4, \infty)$ . $\newline$ Sign of $(x - 1)$ : + $\newline$ Sign of $(x - 4)$ : + $\newline$ Sign of $(x - 1)(x - 4)$ : $(+)(+) = +$
Compound Inequality: $(x - 1)(x - 4) \geq 0$ $\newline$ Find the solution as a compound inequality. $\newline$ $(x - 1)(x - 4)$ is non-negative over $(-\infty, 1]$ and $[4, \infty)$ . $\newline$ Compound inequality: $x \leq 1$ or $x \geq 4$

More problems from Solve quadratic inequalities

Question

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\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

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Posted 2 months ago

Question

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(x - 1)(x + 1) > 0

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Write a compound inequality like

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Question

A particular company charges advertisers a one time cost of

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\newline

\newline

500+4.50M\geq5,000

\newline

4.50+500M>5,000

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500+4.50M\leq5,000

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500+4.50M<5,000

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Question

7x+1 < x+9

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

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1

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x > \frac{4}{3}

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Question

52-3x < -14

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

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1

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x > -\frac{38}{3}

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x > \frac{38}{3}

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Question

5-3x > 2x+2

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

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1

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x < \frac{7}{5}

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x < 3

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x < \frac{3}{5}

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x > \frac{3}{5}

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Question

Rani is a real estate agent. For each house she sells, she pays

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of the selling price of the house. Rani's total profit from a particular house is

\$ 4,580

p

represents the selling price of the house, which equation best models the situation?

\newline

1

\newline

0.018 p-100=4580

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0.018 p+100=4580

\newline

(100-0.018) p=4580

\newline

(100+0.018) p=4580

Posted 2 months ago

Question

A commercial airplane that is

1

500

2

500

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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?

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1

\mathrm{knot}=1.15

miles per hour (mph)

\newline

1

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1,500+690 h=2,500

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1,500+600 h=2,500

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1,500-600 h=2,500

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1,500-690 h=2,500

Posted 1 month ago

Question

A weeping willow that is

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feet in height grows to a maximum height of

35

y

years at a constant rate of

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

Posted 4 months ago

Question

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23

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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

1

\newline

13-\frac{23 h}{60}=10

\newline

13-\frac{60 h}{23}=10

\newline

\frac{13-60 h}{23}=10

\newline

\frac{13-23 h}{60}=10

Posted 3 months ago