Let n is the positive even integer.

Let three consecutive positive even integers are .

The word no greater than represents .

The word Three consecutive positive even integers with a sum no greater than 36 represents .

The inequality is .

Combine like terms

Apply subtraction property of inequality: If then .

Subtract 6 from each side.

Apply division property of inequality: If then .

Divide each side by 3.

Cancel common terms.

.

Therefore n values set is .

If then remaining consecutive positive even numbers are and the inequality solution set is .

If then remaining consecutive positive even numbers are and the inequality solution set is .

If then remaining consecutive positive even numbers are and the inequality solution set is .

If then remaining consecutive positive even numbers are and the inequality solution set is .

If then remaining consecutive positive even numbers are and the inequality solution set is .

The inequality solution sets are .