What is the solution set for the given inequality if the replacement set for r is {5, 6, 7, 8, 9, 10}?

Question

3r ≤ 4r – 6

Answer 1

To find the solution set for the inequality 3r ≤ 4r - 6, we substitute each value from the replacement set for r and determine if it satisfies the inequality.

For r = 5:
3(5) ≤ 4(5) - 6
15 ≤ 20 - 6
15 ≤ 14 (false)

For r = 6:
3(6) ≤ 4(6) - 6
18 ≤ 24 - 6
18 ≤ 18 (true)

For r = 7:
3(7) ≤ 4(7) - 6
21 ≤ 28 - 6
21 ≤ 22 (true)

For r = 8:
3(8) ≤ 4(8) - 6
24 ≤ 32 - 6
24 ≤ 26 (true)

For r = 9:
3(9) ≤ 4(9) - 6
27 ≤ 36 - 6
27 ≤ 30 (true)

For r = 10:
3(10) ≤ 4(10) - 6
30 ≤ 40 - 6
30 ≤ 34 (true)

The values 6, 7, 8, 9, and 10 satisfy the inequality, so the solution set is {6, 7, 8, 9, 10}.