Inequality Proof: Solving for ab > cb with Number Line Diagram

Solution: From the diagram, we can see that 'a < b < 0' and 'c > 0'.

Option A, 'a < b', when multiplying both sides of the inequality by a positive number, the direction of the inequality remains the same. So we would have 'ac < bc'. Therefore, this option is incorrect.

Option B, 'ab > cb', which is true based on the positions of 'a', 'b', and 'c' on the number line. Therefore, this option is correct.

Option C, 'a < b', when adding the same number to both sides of the inequality, the direction of the inequality remains the same. So we would have 'a+c < b+c'. Therefore, this option is incorrect.

Option D, 'a < c', when adding the same number to both sides of the inequality, the direction of the inequality remains the same. So we would have 'a+b < c+b'. Therefore, this option is incorrect.

Therefore, the correct option is B.