Let n is an unknown number.

The word two thirds of a number n added to six represents .

The word is at least represents .

The word Two thirds of a number n added to six is at least twenty - two represents .

The inequality is .

Apply subtraction property of inequality: If .

Subtract 6 from each side.

Apply multiplication property of inequality: If .

Multiply each side by .

Cancel common terms.

The solution set is .

Check:

To check, substitute three different values for n into the original inequality: 24, a number less than 24, and greater than 24.

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 .