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?
Responses
22.5
23.5
22
23
To determine which value of r makes the inequality 3r - 47.5 > 21.5 true, we can solve the inequality just like with an equation.
Starting with the equation 3r - 47.5 = 21.5:
Add 47.5 to both sides:
3r = 69
Divide both sides by 3:
r = 23
Now, substitute the possible values of r into the inequality 3r - 47.5 > 21.5 to see if they make the inequality true.
For r = 22.5:
3(22.5) - 47.5 > 21.5
67.5 - 47.5 > 21.5
20 > 21.5
This is not true, so 22.5 is not the correct value.
For r = 23.5:
3(23.5) - 47.5 > 21.5
70.5 - 47.5 > 21.5
23 > 21.5
This is true, so 23.5 is the correct value.
For r = 22:
3(22) - 47.5 > 21.5
66 - 47.5 > 21.5
18.5 > 21.5
This is not true, so 22 is not the correct value.
Finally, for r = 23:
3(23) - 47.5 > 21.5
69 - 47.5 > 21.5
21.5 > 21.5
This is not true, so 23 is not the correct value.
Therefore, the only value that makes the inequality 3r - 47.5 > 21.5 true is r = 23.5.
To find which value of r makes the inequality 3r - 47.5 > 21.5 true, we can solve the inequality for r.
3r - 47.5 > 21.5
First, add 47.5 to both sides:
3r - 47.5 + 47.5 > 21.5 + 47.5
3r > 69
Next, divide both sides by 3:
3r/3 > 69/3
r > 23
Therefore, any value of r greater than 23 will make the inequality 3r - 47.5 > 21.5 true.
The correct response is 23.5.