Let n is an unknown number.

The word four times a number n minus 6 represents .

The word is greater than represents .

The word eight plus two times the number n represents .

The word Four times a number n minus 6 is greater than eight plus two times the number n represents .

The inequality is .

Apply subtraction property of inequality: If .

Subtract 2n from each side.

Apply addition property of inequality: If .

Add 6 to each side.

Apply division property of inequality: If .

Divide each side by 2.

The solution set is .

Check:

To check, substitute three different values for n into the original inequality: 7, a number less than 7, and greater than 7.

Let three values are .

If then (This is false)

If then (This is false)

If then (This is true).

The inequality is and the solution set is .