Question

solve the equation. check your solution.
\\(\frac{3}{14}x + \frac{2}{7} = \frac{1}{7}x\\)
\\(\big\\{-4\big\\}
\big\\{-6\big\\}
\big\\{4\big\\}
\big\\{6\big\\}\\)

Explanation:

Step1: Isolate x terms on left

Subtract $\frac{1}{7}x$ from both sides.
$\frac{3}{14}x - \frac{1}{7}x + \frac{2}{7} = 0$

Step2: Convert to common denominator

Rewrite $\frac{1}{7}x$ as $\frac{2}{14}x$.
$\frac{3}{14}x - \frac{2}{14}x + \frac{2}{7} = 0$

Step3: Simplify x terms

Combine like x terms.
$\frac{1}{14}x + \frac{2}{7} = 0$

Step4: Isolate the x term

Subtract $\frac{2}{7}$ from both sides.
$\frac{1}{14}x = -\frac{2}{7}$

Step5: Solve for x

Multiply both sides by 14.
$x = -\frac{2}{7} \times 14$

Step6: Calculate final x value

Simplify the right-hand side.
$x = -4$

Step7: Verify the solution

Substitute $x=-4$ into original equation.
$\frac{3}{14}(-4) + \frac{2}{7} = \frac{1}{7}(-4)$
$-\frac{12}{14} + \frac{4}{14} = -\frac{4}{7}$
$-\frac{8}{14} = -\frac{4}{7}$
$-\frac{4}{7} = -\frac{4}{7}$ (True)

Answer:

A. {-4}