To simplify the expression [tex]\(-\frac{1}{7}(-3x + 7)\)[/tex], we will distribute [tex]\(-\frac{1}{7}\)[/tex] to each term inside the parentheses. Here are the steps:
1. Distribute [tex]\(-\frac{1}{7}\)[/tex] to [tex]\(-3x\)[/tex]:
[tex]\[
-\frac{1}{7} \cdot (-3x) = \frac{3}{7}x
\][/tex]
Explanation: Multiplying [tex]\(-\frac{1}{7}\)[/tex] by [tex]\(-3x\)[/tex] results in a positive value because multiplying two negative numbers yields a positive result. Therefore, [tex]\(-\frac{1}{7} \cdot -3x = \frac{3}{7}x\)[/tex].
2. Distribute [tex]\(-\frac{1}{7}\)[/tex] to [tex]\(7\)[/tex]:
[tex]\[
-\frac{1}{7} \cdot 7 = -1
\][/tex]
Explanation: Multiplying [tex]\(-\frac{1}{7}\)[/tex] by [tex]\(7\)[/tex] results in [tex]\(-1\)[/tex]. This is because [tex]\(7 \cdot \frac{1}{7} = 1\)[/tex] and the negative sign makes it [tex]\(-1\)[/tex].
3. Combine the simplified terms:
[tex]\[
\frac{3}{7}x - 1
\][/tex]
So, the simplified expression is:
[tex]\[
\frac{3}{7} x - 1
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{3}{7} x - 1}
\][/tex]
This corresponds to option D.
