We are given the equation:

$2.5(y - x) = 0$

And we're told that when the solution is $y = 6$, we need to find what must be true about $x$.

Step 1: Analyze the equation

The given equation is:

$2.5(y - x) = 0$

Since we know $y = 6$, substitute $y = 6$ into the equation:

$2.5(6 - x) = 0$

Step 2: Solve for $x$

Now simplify the equation:

$6 - x = 0$

Solving for $x$, we find:

$x = 6$

Conclusion:

For the equation $2.5(y - x) = 0$ to hold true with $y = 6$, the value of $x$ must also be $6$.

Justification:

The equation $2.5(y - x) = 0$ implies that $(y - x)$ must be zero because multiplying by 2.5 doesn't affect the equality. Thus, for $y = 6$, we must have $6 - x = 0$, which leads to $x = 6$.

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Would you like more details on the steps or any clarification? Here are some related questions:

1. What happens to the equation if $y \neq 6$?
2. How does multiplying an equation by a constant affect its solution?
3. What other equations would have the same solution for $x$?
4. How would you solve similar equations with different constants (like 3.5 or 1.5)?
5. What are some other common forms of equations that require finding the value of $x$?

Tip: Always check whether a constant multiplication in an equation can be simplified or factored out to make solving easier.