To solve the equation [tex]\(-x + \frac{3}{7} = 2x - \frac{25}{7}\)[/tex], follow these steps:
1. Combine like terms to move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\[
-x + \frac{3}{7} = 2x - \frac{25}{7}
\][/tex]
Add [tex]\(x\)[/tex] to both sides to start isolating [tex]\(x\)[/tex]:
[tex]\[
\frac{3}{7} = 3x - \frac{25}{7}
\][/tex]
2. Move the constant terms to the other side:
Add [tex]\(\frac{25}{7}\)[/tex] to both sides to move all the constants to one side:
[tex]\[
\frac{3}{7} + \frac{25}{7} = 3x
\][/tex]
Combine the fractions on the left-hand side:
[tex]\[
\frac{28}{7} = 3x
\][/tex]
Simplify the fraction:
[tex]\[
4 = 3x
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by [tex]\(3\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{4}{3}
\][/tex]
So, the solution to the equation [tex]\(-x + \frac{3}{7} = 2x - \frac{25}{7}\)[/tex] is:
[tex]\[
x = \frac{4}{3}
\][/tex]
This corresponds to the answer choice [tex]\(B\)[/tex].
