Question

1. what is the minimum value that will make the inequality b - 2 > 13 true? 8. stephen ran in the run disney marathon at walt disney world. he ran a mile at a rate faster than five mph. write an inequality to represent this situation. let x represent the speed that stephen ran. 9. mr. brown’s math test exceeded 20 questions. draw a graph to represent this situation. let x represent the number of questions on the test. 10. is it true that the solution set of an inequality has infinite solutions? defend your answer.

Explanation:

Step1: Solve the first - inequality

Solve $b - 2>13$ for $b$. Add 2 to both sides of the inequality: $b-2 + 2>13 + 2$, so $b>15$. The smallest integer value of $b$ that makes this true is $b = 16$.

Step2: Write the second - inequality

Since Stephen ran at a rate $x$ faster than five mph, the inequality is $x>5$.

Step3: Write the third - inequality and consider graphing

If $x$ represents the number of questions on Mr. Brown's math test and it exceeded 20 questions, the inequality is $x>20$. To graph it on a number - line, draw an open circle at 20 (because 20 is not included in the solution set) and draw an arrow to the right.

Step4: Answer the fourth - question

The solution set of an inequality has infinite solutions. For example, in the inequality $x>5$, numbers like 5.1, 5.01, 5.001, 6, 7, 8, etc. are all solutions. There are an infinite number of real numbers that satisfy the inequality.

Answer:

1. 16
2. $x>5$
3. The inequality is $x > 20$. To graph: Draw an open - circle at 20 on the number line and an arrow pointing to the right.
4. Yes. The solution set of an inequality often has infinite real - number solutions as there are an infinite number of values that can satisfy the inequality relationship.