Question

solve the equation. identify excluded values as appropriate.

\\\frac{3}{7}x = 6\\

select the correct choice below and, if necessary, fill in the answer box within your choice.

a. \\(x = \\) (type an integer or a simplified fraction.)
b. the equation has no solution.

Explanation:

Analyze the given equation

We are given a linear equation to solve:

$$ \frac{3}{7}x = 6 $$

We need to find the value of \(x\) and check for any excluded values.

Identify excluded values

Using the Linear Equations knowledge point

$$ \text{No variables in denominators } \implies \text{No excluded values.} $$

Solve for x

Using the One-Step Equations knowledge point

$$
LATEXBLOCK0
$$

Verify the solution

We substitute \(x = 14\) back into the original equation:

$$ \frac{3}{7}(14) = 3 \cdot 2 = 6 $$

The solution is correct and valid.

Answer:

• (A) \(x = 14\) (Type an integer or a simplified fraction.) (Correct answer)
• (B) The equation has no solution.