Question

solve the equation.
\\(\frac{3}{x} = \frac{6}{16}\\)

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 \(\frac{3}{x}=\frac{6}{16}\), 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 \(3\times16=6\times x\).
So, \(48 = 6x\).

Step2: Solve for x

Divide both sides of the equation \(48 = 6x\) by 6. Using the division property of equality (dividing both sides of an equation by the same non - zero number keeps the equation balanced), we have \(x=\frac{48}{6}\).
Simplifying \(\frac{48}{6}\), we get \(x = 8\).

Answer:

A. The solution is \(x = 8\)