Which inequality models this situation?
What is the simplified rational inequality?
Which below is the first step in solving the rational inequality?
What common denominator can be used to write the left side as one rational expression?10x10 + x10(10 + x)20 + x
Next you need to find the critical points. What are the critical points, and how are they found?
The critical points are −10 and 25. Set the numerator and denominator equal to 0: x − 25 = 0 gives x = 25, and 5(10 + x) = 0 gives x = −10.
Which did you include in your response?
Write a report to the president of the company explaining the meaning of the solutions.
The negative part of the solution is ignored because a negative number of phones cannot be produced. The company must assemble at least 25 more phones that work to reach an 80% success rate. It has 3 working phones out of the 10 already made, so if the next 25 phones work, 28 of 35 phones will work, bringing the company to its goal of 80% on the 35th phone.
As the number of phones produced increases, will the working rate ever get to 100%? Explain.
No. The working rate may get closer to 100% as more phones are produced, and it might eventually round to 100%, but it never actually reaches 100%. The model starts with 3 of 10 phones working, leaving 7 that are not working, so the numerator and denominator are never equal.
Test points for the intervals are shown. Select the test points that make the inequality true.
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