Sure, let's solve this step-by-step.
1. Understand the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
Given that [tex]\(x\)[/tex] is the predecessor of [tex]\(y\)[/tex], it means that [tex]\(x\)[/tex] comes immediately before [tex]\(y\)[/tex]. Thus, [tex]\(x\)[/tex] is one less than [tex]\(y\)[/tex].
Hence, we have the equation:
[tex]\[
x = y - 1
\][/tex]
2. Substitute [tex]\(x\)[/tex] in the expression [tex]\(x - y\)[/tex]:
We want to find the value of [tex]\(x - y\)[/tex]. Using the relationship [tex]\(x = y - 1\)[/tex], substitute [tex]\(x\)[/tex] in the expression [tex]\(x - y\)[/tex]:
[tex]\[
x - y = (y - 1) - y
\][/tex]
3. Simplify the expression:
Now, let's simplify the right-hand side:
[tex]\[
(y - 1) - y = y - 1 - y
\][/tex]
Notice that [tex]\(+y\)[/tex] and [tex]\(-y\)[/tex] cancel each other out:
[tex]\[
y - 1 - y = -1
\][/tex]
Therefore, the value of [tex]\( x - y \)[/tex] is:
[tex]\[
-1
\][/tex]
