Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $c$ . $\newline$ |5c| > 5 $\newline$ 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. $\newline$ ______

View step-by-step help

View step-by-step help

Solve absolute value inequalities

Full solution

Q. Solve for

c

.

\newline

|5c| > 5

\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

______

Given Inequality: We have the inequality: $\newline$ |5c| > 5 $\newline$ First, we solve for $|5c|$ . $\newline$ |5c| > 5 $\newline$ This means that $5c$ is either greater than $5$ or less than $-5$ .
Case $1$ : Now we split the inequality into two cases: $\newline$ Case $1$ : When $5c$ is positive, we have: $\newline$ 5c > 5 $\newline$ Now we divide both sides by $5$ to solve for $c$ : $\newline$ \frac{5c}{5} > \frac{5}{5} $\newline$ c > 1
Case $2$ : Case $2$ : When $5c$ is negative, we have: $\newline$ 5c < -5 $\newline$ Again, we divide both sides by $5$ to solve for $c$ : $\newline$ \frac{5c}{5} < \frac{-5}{5} $\newline$ c < -1
Combined Solution: Combining both cases, we get the compound inequality: $\newline$ c < -1 or c > 1 $\newline$ This is the solution to the inequality |5c| > 5.

More problems from Solve absolute value inequalities

Question

s

\newline

|s| + 3 \geq 8

Posted 5 months ago

Question

Which compound inequality represents the value of

x ?

\newline

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

\newline

Posted 5 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

\newline

500+4.50M\geq5,000

\newline

4.50+500M>5,000

\newline

500+4.50M\leq5,000

\newline

500+4.50M<5,000

Posted 8 months ago

Question

7x+1 < x+9

\newline

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

\newline

1

\newline

x > \frac{4}{3}

\newline

x < \frac{4}{3}

\newline

x < 1

\newline

x < \frac{5}{3}

Posted 4 months ago

Question

52-3x < -14

\newline

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

\newline

1

\newline

x > -\frac{38}{3}

\newline

x > \frac{38}{3}

\newline

x < 22

\newline

x > 22

Posted 10 months ago

Question

5-3x > 2x+2

\newline

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

\newline

1

\newline

x < \frac{7}{5}

\newline

x < 3

\newline

x < \frac{3}{5}

\newline

x > \frac{3}{5}

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

p

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

\newline

1

\newline

0.018 p-100=4580

\newline

0.018 p+100=4580

\newline

(100-0.018) p=4580

\newline

(100+0.018) p=4580

Posted 8 months ago

Question

A commercial airplane that is

1

500

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

1

\newline

1,500+690 h=2,500

\newline

1,500+600 h=2,500

\newline

1,500-600 h=2,500

\newline

1,500-690 h=2,500

Posted 7 months ago

Question

A weeping willow that is

15

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 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

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 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant