From the set {10.2, 18.9, 13.4}, use substitution to determine which value of x makes the inequality true.

r - 2.9 > 13.5

A. 10.2

B. 18.9

C. none of these

D. 13.1

Let's plug in r = 10.2 to see if we get a true inequality or not

r - 2.9 > 13.5

10.2 - 2.9 > 13.5

7.3 > 13.5

The last inequality is false because 7.3 is not greater than 13.5

So we can rule out choice A

Now let's try out r = 18.9 from choice B

r - 2.9 > 13.5

18.9 - 2.9 > 13.5

16 > 13.5

This is true, so the original inequality is true when r = 18.9

Choice C is ruled out because choice B is the answer.

For the sake of completeness, let's try out choice D

Plug in r = 13.1 to get...

r - 2.9 > 13.5

13.1 - 2.9 > 13.5

10.2 > 13.5

We get a false statement, so r = 13.1 is not a solution

Choice D is ruled out. We can add 2.9 to both sides in the original inequality to get r > 16.4, which helps back up why choice B is the answer.

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