Select the correct answer.

What is the solution for [tex]\( x \)[/tex] in the equation?
[tex]\[
-x + \frac{3}{7} = 2x - \frac{25}{7}
\][/tex]

A. [tex]\( x = \frac{3}{4} \)[/tex]

B. [tex]\( x = -\frac{4}{3} \)[/tex]

C. [tex]\( x = \frac{4}{3} \)[/tex]

D. [tex]\( x = -\frac{3}{4} \)[/tex]



Answer :

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].