Question

solve the equation.
\\(\frac{2}{x} = \frac{4}{14}\\)

select the correct choice below and fill in any answer boxes present in your choice.

a. the solution is \\(x = \square\\).
(type an integer or a simplified fraction. use a comma to separate answers as needed.)

b. there is no solution.

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{2}{x}=\frac{4}{14}\), cross - multiplying (which is based on the property of proportions: if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\)) gives us \(2\times14=4\times x\).

Step2: Simplify both sides

Simplify the left - hand side: \(2\times14 = 28\), so the equation becomes \(28 = 4x\).

Step3: Solve for x

Divide both sides of the equation \(28 = 4x\) by 4. \(\frac{28}{4}=\frac{4x}{4}\), which simplifies to \(x = 7\). We need to check if \(x = 7\) is valid. Since the original equation has \(x\) in the denominator, \(x
eq0\), and \(7
eq0\), so \(x = 7\) is a valid solution.

Answer:

A. The solution is \(x = 7\)