Verification of (x-y) not equal to (y-x)

First, let's substitute the given values of x and y into the expressions (x-y) and (y-x) to see if they are equal or not.

Substituting x = -4/7 and y = 2/5 into (x-y):
(x-y) = (-4/7) - (2/5)

To simplify the expression, we need to find a common denominator for the fractions, which is 35.

(x-y) = (-20/35) - (14/35)
(x-y) = (-20 - 14)/35
(x-y) = -34/35

Next, let's substitute x = -4/7 and y = 2/5 into (y-x):
(y-x) = (2/5) - (-4/7)

Again, we need to find a common denominator for the fractions, which is 35.

(y-x) = (14/35) - (-20/35)
(y-x) = (14 + 20)/35
(y-x) = 34/35

Comparison of (x-y) and (y-x)

By comparing the expressions (x-y) = -34/35 and (y-x) = 34/35, we can see that they are NOT equal.

Explanation:

When we subtract y from x, we get a negative value of -34/35. On the other hand, when we subtract x from y, we get a positive value of 34/35. This difference in sign indicates that the two expressions are not equal.

In general, when subtracting two numbers, the order of subtraction matters. The result will be different depending on the order in which the numbers are subtracted.

The property of subtraction, called non-commutativity, states that the order of subtraction affects the result. This property is demonstrated in this case, where (x-y) and (y-x) give different values.

Therefore, we have verified that (x-y) is not equal to (y-x) using the given values of x = -4/7 and y = 2/5.