Let n is an unknown number.

The word the sum of three times a number n and represents .

The word is at least represents .

The word twice the number n plus 8 represents .

The word The sum of three times a number n and is at least twice the number n plus 8. represents .

The inequality is .

Apply subtraction property of inequality: If .

Subtract 2n from each side.

Apply commutative property of addition: If .

Apply addition property of inequality: If .

Add 4 to each side.

The solution set is .

Check:

To check, substitute three different values for n into the original inequality: 12, a number less than 12, and greater than 12.

Let three values are .

If then (This is false)

If then (This is true)

If then (This is true).

The inequality is and the solution set is .