Let n is an unknown number.

The word the product of and a number n represents.

The word is greater than represents.

The word is less than represents.

The word the product of and a number n is greater than 35 or is less than represents.

The compound inequality is .

Solve the inequality 1: .

Divide each side by negative 5 and reverse the inequality.

Cancel common terms.

.

Solve the inequality 2: .

Divide each side by negative 5 and reverse the inequality.

Cancel common terms.

.

The solution set is .

The value of n lies between .

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

Let three values are .

If then (This is true)

If then (This is false)

If then (This is false)

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

Let three values are .

If then (This is false)

If then (This is false)

If then    (This is true)

The solution set is .