Does the system −12 + 3x > 0 and 9 − 4x > −3 have any solutions?

Question

Find the solution of the system:

• −12 + 3x > 0;
• 9 − 4x > −3.

Answer choices

Option 1: no solutions.

Option 2: 3 < x < 4.

Option 3: x > 4.

Option 4: x < 3.

Explanation

The first inequality gives 3x > 12, so x > 4.

The second gives −4x > −12. Dividing by a negative number reverses the inequality: x < 3.

A number cannot be greater than 4 and less than 3 at the same time. The intersection of the solution sets is empty: ∅.