Question

solve the equation.
\\(\frac{7}{x} = \frac{35}{30}\\)

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 $\frac{7}{x}=\frac{35}{30}$, 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 $7\times30 = 35\times x$.

Step2: Simplify and solve for x

First, calculate $7\times30 = 210$. So the equation becomes $210 = 35x$. Then, divide both sides of the equation by 35 to solve for $x$. We have $x=\frac{210}{35}$. Simplifying $\frac{210}{35}$, we know that $35\times6 = 210$, so $x = 6$.

Answer:

A. The solution is $x = 6$