Let n is an unknown number.

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

The word is less than or equal to represents .

The word the sum of twenty - four and ten times the number n represents .

The word The sum of nine times a number n and fifteen is less than or equal to the sum of twenty - four and ten times the number n represents .

The inequality is .

Apply subtraction property of inequality: If .

Subtract 9n from each side.

Subtract 24 from each side.

The solution set is .

Check:

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

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 .