Let's simplify the given expression step-by-step:
We start with the expression:
[tex]\[
8 - 4(-x + 5)
\][/tex]
First, distribute the \(-4\) to both terms inside the parentheses:
[tex]\[
8 - 4(-x) + (-4)(5)
\][/tex]
Simplify each part of the distribution:
[tex]\[
8 - (-4x) - 20
\][/tex]
Remember that subtracting a negative is the same as adding a positive:
[tex]\[
8 + 4x - 20
\][/tex]
Combine like terms by adding and subtracting the constants:
[tex]\[
8 - 20 + 4x
\][/tex]
[tex]\[
-12 + 4x
\][/tex]
Rewriting the expression in standard form (terms in descending order of their degree), we get:
[tex]\[
4x - 12
\][/tex]
Hence, the simplified form of the given expression is:
[tex]\[
4x - 12
\][/tex]
Now we match this with the given options:
- (A) \(4x - 12\)
- (B) \(-4x - 12\)
- (C) \(4x + 13\)
- (D) \(4x + 5\)
The correct answer is option (A):
[tex]\[
4x - 12
\][/tex]
