Let n is an unknown number.

The word one half a number n represents.

The word is greater than represents.

The word is less than or equal represents.

The word one half a number n is greater than 0 represents.

The word one half a number n is less than or equal to 1 represents.

The word one half a number n is greater than 0 and less than or equal to 1 represents.

The compound inequality is .

The compound inequality divided into two inequalities by using and.

Solve the inequality 1: .

Multiply each side by 2.

Cancel common terms.

.

Solve the inequality 2: .

Multiply each side by 2.

Cancel common terms.

.

The solution set is .

The value of n lies between include 2.

Check: To check, substitute three different values for n into the original compound inequality : any number between include 2, a number less than equal 0, and greater than 2.

Let five values are .

If then (This is false).

If then (This is false).

If then (This is true).

If then     (This is true).

If then (This is false).

The solution set is .