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Which values from the given replacement set make up the solution set of the inequality?

5n>24 ; {2, 3, 4, 5, 6}



Responses

{3, 4}
left curly bracket 3 comma 4 right curly bracket

{5, 6}
left curly bracket 5 comma 6 right curly bracket

{2, 3}
left curly bracket 2 comma 3 right curly bracket

{4, 5, 6}

1 answer

To solve the inequality \( 5n > 24 \), we can first isolate \( n \):

\[ n > \frac{24}{5} \] \[ n > 4.8 \]

Now, we will check the values in the replacement set {2, 3, 4, 5, 6} to see which ones satisfy the inequality \( n > 4.8 \):

  • For \( n = 2 \): \( 5(2) = 10 \) (not greater than 24)
  • For \( n = 3 \): \( 5(3) = 15 \) (not greater than 24)
  • For \( n = 4 \): \( 5(4) = 20 \) (not greater than 24)
  • For \( n = 5 \): \( 5(5) = 25 \) (greater than 24)
  • For \( n = 6 \): \( 5(6) = 30 \) (greater than 24)

The values that satisfy the inequality \( 5n > 24 \) are \( n = 5 \) and \( n = 6 \).

Thus, the solution set is:

\({5, 6}\)

So, the correct response is:

{5, 6}