Solve and check your solution. \[ \frac{5}{7}=\frac{1}{7}+3 x \] \( x=\square \) (Type an integer or a simplified fraction.)

To solve the equation \( \frac{5}{7} = \frac{1}{7} + 3x \), first, subtract \( \frac{1}{7} \) from both sides: \[ \frac{5}{7} - \frac{1}{7} = 3x \] This simplifies to: \[ \frac{4}{7} = 3x \] Next, divide both sides by 3 to isolate \( x \): \[ x = \frac{4}{7} \div 3 \] This can be rewritten as: \[ x = \frac{4}{7} \cdot \frac{1}{3} = \frac{4}{21} \] So the solution is: \( x = \frac{4}{21} \) To check the solution, substitute \( x \) back into the original equation: \[ \frac{5}{7} = \frac{1}{7} + 3 \left(\frac{4}{21}\right) \] First calculating \( 3 \left(\frac{4}{21}\right) \): \[ 3 \cdot \frac{4}{21} = \frac{12}{21} = \frac{4}{7} \] Thus, \[ \frac{5}{7} = \frac{1}{7} + \frac{4}{7} \] Adding the right side: \[ \frac{1}{7} + \frac{4}{7} = \frac{5}{7} \] Since both sides are equal, the solution is verified. \( x = \frac{4}{21} \)