If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?

The correct option is (y – x) is less than or equal to 15.

Let's break down the given information step-by-step to understand why this option is always correct:
We are given two inequalities:
1. $x\ge 25$ (which means x is greater than or equal to 25)
2. $y\le 40$ (which means y is less than or equal to 40)

To analyze the expression $y-x$, we want to determine its maximum possible value. The value of the difference $y-x$ is maximized when we take the largest possible value of $y$ and subtract the smallest possible value of $x$.

From our given inequalities:
- The maximum possible value for $y$ is 40.
- The minimum possible value for $x$ is 25.

Now, we calculate the maximum value of $y-x$ by substituting these boundary values:
$\text{Maximum of}(y-x)=\text{Maximum of}y-\text{Minimum of}x$
$\text{Maximum of}(y-x)=40-25=15$

Alternatively, we can derive this using algebraic manipulation of the inequalities:
Start with the inequality for $x$:
$x\ge 25$

Multiply both sides of the inequality by -1. Remember that multiplying an inequality by a negative number reverses the inequality sign:
$-x\le -25$

Now, we add this to the inequality for $y$:
$y\le 40$

Adding the two corresponding sides of the inequalities gives:
$y-x\le 40-25$
$y-x\le 15$

Since the maximum possible value of $y-x$ is 15, the value of $y-x$ will always be less than or equal to 15. Therefore, the statement (y – x) is less than or equal to 15 is always correct.