If 3xm + 2ym − 2yn − 3xn = 0 and m ≠ n , then what is the value of y in terms of x?

To answer this question, we will need to use an approach that is called “Factoring by Grouping.” We can use this approach when we have 4 terms and there is a pattern between 2 of the terms.

**Step 1: Re-arrange terms**

To begin, we will rewrite the equation as:

3xm – 3xn + 2ym – 2yn = 0

**Step 2: Factor**

Then, we will factor:

3x (m-n) + 2y (m-n) = 0

**Step 3: Simplify**

Because we have (m-n) in both places, we can simplify to:

(3x + 2y) (m -n) = 0

**Step 4: Solve**

Since the equation is equal to zero, we can conclude that either 3x + 2y = 0 or m-n = 0. However, for m-n=0 then it must be true that m=n and the question prompt says that is not true.

Therefore, if 3x + 2y = 0 we can subtract -3x from both sides and divide both sides by 2. This is the correct answer, -3x/2.