To evaluate [tex]\((-4)(-7)\)[/tex] using the defined operation [tex]\(ab = |2a - 2b + 5|\)[/tex], follow these steps:
1. Identify the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]. Here, [tex]\(a = -4\)[/tex] and [tex]\(b = -7\)[/tex].
2. Substitute these values into the defined operation [tex]\(ab = |2a - 2b + 5|\)[/tex].
3. Substitute [tex]\(a = -4\)[/tex] and [tex]\(b = -7\)[/tex] into the expression inside the absolute value:
[tex]\[
2a - 2b + 5 = 2(-4) - 2(-7) + 5
\][/tex]
4. Simplify the expression:
[tex]\[
2(-4) - 2(-7) + 5 = -8 + 14 + 5
\][/tex]
5. Further simplify the expression:
[tex]\[
-8 + 14 + 5 = 6 + 5 = 11
\][/tex]
6. Apply the absolute value (though it is already positive in this case):
[tex]\[
|11| = 11
\][/tex]
Therefore, the result of [tex]\((-4)(-7)\)[/tex] using the given operation is [tex]\(\boxed{11}\)[/tex].
