To solve the equation [tex]\( -x + \frac{3}{7} = 2x - \frac{25}{7} \)[/tex], we can follow these steps:
1. Combine like terms involving [tex]\( x \)[/tex]:
[tex]\[
-x - 2x + \frac{3}{7} = -\frac{25}{7}
\][/tex]
Simplifying the [tex]\( x \)[/tex]-terms on the left-hand side:
[tex]\[
-3x + \frac{3}{7} = -\frac{25}{7}
\][/tex]
2. Move constant terms to one side of the equation:
To isolate the terms with [tex]\( x \)[/tex], we can subtract [tex]\(\frac{3}{7}\)[/tex] from both sides:
[tex]\[
-3x = -\frac{25}{7} - \frac{3}{7}
\][/tex]
Combining the fractions on the right-hand side:
[tex]\[
-3x = -\frac{28}{7}
\][/tex]
Simplifying the fraction:
[tex]\[
-3x = -4
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides by [tex]\(-3\)[/tex] to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{4}{3}
\][/tex]
Thus, the solution for [tex]\( x \)[/tex] in the given equation is:
[tex]\[
x = \frac{4}{3}
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{C} \)[/tex].
