Let n is an unknown number.

The word eight times a number n minus twenty - seven represents .

The word is no more than represents .

The word the negative of that number n plus eighteen represents .

The word Eight times a number n minus twenty - seven is no more than the negative of that number n plus eighteen represents .

The inequality is .

Apply addition property of inequality: If .

Add n to each side.

Add 27 to each side.

Apply division property of inequality: If .

Divide each side by 9.

Cancel common terms.

The solution set is .

Check:

To check, substitute three different values for n into the original inequality: 5, a number less than 5, and greater than 5.

Let three values are .

If then (This is true)

If then (This is true)

If then (This is false).

The inequality is and the solution set is .