Let n is an unknown number.

The word three fourths of a number n decreased by nine represents .

The word is at least represents .

The word Three fourths of a number n decreased by nine is at least forty two represents .

The inequality is .

Apply addition property of inequality: If .

Add 9 to each side.

Apply multiplication property of inequality: If .

Multiply each side by .

Cancel common terms.

Cancel common terms.

The solution set is .

Check:

To check, substitute three different values for n into the original inequality: 68, a number less than 68, and greater than 68.

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 .