Question

For the inequality 5k>100, Keegan says that both 20 and 100 are solutions. Is he correct? Explain why or why not.

A) Keegan is correct; both 20 and 100 are solutions to the inequality.
B) Keegan is not correct; only 100 is a solution to the inequality.
C) Keegan is not correct; neither 20 nor 100 is a solution to the inequality.
D) Keegan is not correct; only 20 is a solution to the inequality.

Answer 1

Keegan is not correct. 20 is not a solution to the inequality 5k > 100 because 5(20) equals 100, which is not greater than 100. However, 100 is a solution since 5(100) equals 500, which is greater than 100.

Step-by-step explanation:

To determine whether Keegan's assertion about the inequality 5k > 100 is correct, we need to test each value he proposes and see if they satisfy the inequality. For a value to be a solution, when substituted into the inequality, the resulting statement must hold true.

Let's test 20 first: 5(20) = 100. This gives us the statement 100 > 100, which is not true, because 100 is not greater than 100; it is equal to it. Thus, 20 is not a solution to the inequality.

Next, we test 100: 5(100) = 500. This gives us the statement 500 > 100, which is true. Hence, 100 is a solution to the inequality.

Therefore, Keegan is not correct; only 100 is a solution to the inequality, making the correct answer D) Keegan is not correct; only 20 is a solution to the inequality.