Rational Inequalities

Question 1

Which inequality models this situation?

Revolt · Accepted Answer

D:

Question 2

Which below is the first step in solving the rational inequality?

Revolt · Accepted Answer

A:

Question 3

Next you need to find the critical points. What are the critical points, and how are they found?

Revolt · Accepted Answer

The critical points are the values that make the numerator or the denominator of the rational expression equal to zero. To find them, you set the numerator equal to zero and solve for the variable, an

Question 4

Write a report to the president of the company explaining the meaning of the solutions.

Revolt · Accepted Answer

The negative part of the solution set is ignored, because you cannot produce a negative number of phones. The company has at least an 80% success rate if the next 25 or more phones that are assembled work. Because the company has already made 10 phones and 7 are not working, if the next 25 phones work, the 35th phone puts the company at its goal of 80% or more.

Question 5

What percent is reached if (round answers to the nearest tenth of a percent):The next 50 phones are working? ⇒ 88.3%The next 100 phones are working? ⇒ 93.6%The next 500 phones are working? ⇒ 98.6%

Revolt · Accepted Answer

98.6

Question 6

As the number of phones produced increases, will the working rate ever get to 100%? Explain.

Revolt · Accepted Answer

Although the percentage might eventually round to 100%, it is not possible to have 100% of the phones working. This is because the model began when only 3 out of 10 phones were working, so there are 7 phones that were not working. In other words, the numerator and denominator of the expression are never the same, so the expression is never equal to 1 or 100%.

Question 7

What common denominator can be used to write the left side as one rational expression?10x10 + x✔ 10(10 + x)20 + x

Revolt · Accepted Answer

D: ✔ 10(10 + x)

Question 8

Which did you include in your response?

Revolt · Accepted Answer

A: The critical points are found by setting the numerator and denominator equal to 0.; B: The critical points are at –10 and 25.

Question 9

Does your report include the following?The negative part of the solution set is ignored, because you cannot produce a negative number of phones.The company has at least an 80% success rate if the next 25 or more phones that are assembled work.Because the company has already made 10 phones and 7 are not working, if the next 25 phones work, the 35th phone puts the company at its goal of 80% or more.

Revolt · Accepted Answer

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Question 10

Check all facts below that you included in your response.Although the percentage might eventually round to 100%, it is not possible to have 100% of the phones working.This is because the model began when only 3 out of 10 phones were working, so there are 7 phones that were not working. In other words, the numerator and denominator of the expression are never the same, so the expression is never equal to 1 or 100%.

Revolt · Accepted Answer

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Rational Inequalities Answers

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