When the value of r is 23, the equation 3r−47.5=21.5 is a true statement. Which of the following values of r makes the inequality 3r−47.5>21.5 a true statement? (1 point)

Question

Responses

23.5
23.5

22
22

22.5
22.5

23
23
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Answer 1

To determine which value of \( r \) makes the inequality \( 3r - 47.5 > 21.5 \) a true statement, let's first solve the inequality.

Starting with the inequality:

\[ 3r - 47.5 > 21.5 \]

Add \( 47.5 \) to both sides:

\[ 3r > 21.5 + 47.5 \] \[ 3r > 69 \]

Now, divide both sides by \( 3 \):

\[ r > 23 \]

The value of \( r \) must be greater than \( 23 \) for the inequality to be true. Now, let's evaluate the provided options:

1. \( 23.5 \) (True, since \( 23.5 > 23 \))
2. \( 22 \) (False, since \( 22 < 23 \))
3. \( 22.5 \) (False, since \( 22.5 < 23 \))
4. \( 23 \) (False, since \( 23 \) is equal to \( 23 \))

The only value of \( r \) that satisfies the inequality \( 3r - 47.5 > 21.5 \) is:

23.5.