To find the value of [tex]\(7 \Delta 4\)[/tex], we need to evaluate the expression [tex]\(7 \Delta 4\)[/tex] using the given operation definition [tex]\(x \Delta y = 2[x - 2(y - x)]\)[/tex].
Here are the steps:
1. First, substitute [tex]\(x = 7\)[/tex] and [tex]\(y = 4\)[/tex] into the operation definition:
[tex]\[
x \Delta y = 2[7 - 2(4 - 7)]
\][/tex]
2. Simplify the expression inside the brackets first:
[tex]\[
4 - 7 = -3
\][/tex]
3. Next, multiply by 2:
[tex]\[
2(-3) = -6
\][/tex]
4. Now, substitute back into the expression:
[tex]\[
7 - (-6) = 7 + 6 = 13
\][/tex]
5. Finally, multiply by 2:
[tex]\[
2(13) = 26
\][/tex]
Therefore, [tex]\(7 \Delta 4 = 26\)[/tex].
