Let n is an unknown number.

The word the sum of a number n and seven represents .

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

The word is greater than represents .

The word five times the number n less thirteen represents .

The word Three times the sum of a number n and seven is greater than five times the number n less thirteen represents .

The inequality is .

Apply distributive property: .

Apply subtraction property of inequality: If .

Subtract 3n from each side.

Apply addition property of inequality: If .

Add 13 to each side.

Apply division property of inequality: If .

Divide each side by 2.

Cancel common terms.

The solution set is .

Check:

To check, substitute three different values for n into the original inequality: 17, a number less than 17, and greater than 17.

Let three values are .

If then (This is true)

If then (This is false)

If then (This is false).

The inequality is and the solution set is .