Question

For which of the following inequalities is the solution set true?{0,1,2,3,4,5}4k + 5 > 20k/3 - 4 < 849.7k <_ -9k - 9.4

Answer 1

k/3 - 4 < 8

Substituting all the elements of the set into the inequality is true as shown below

When k is 0

k/3 - 4 < 8

0/3 -4 < 8

-4 < 8

When k is 1

k/3 - 4 < 8

1/3 -4 < 8

-3 2/3 < 8

When k is 2

k/3 - 4 < 8

2/3 -4 < 8

- 3 1/3 < 8

When k is 3

k/3 - 4 < 8

3/3 -4 < 8

-3 < 8

When k is 4

k/3 - 4 < 8

4/3 -4 < 8

-2 2/3 < 8

When k is 5

k/3 - 4 < 8

5/3 -4 < 8

-2 1/3 < 8

Hence the proof