Solving the Proportion: \frac{3}{7} = \frac{9}{x}

Understanding how to solve equations involving fractions is a fundamental skill in algebra. One common type of problem students encounter is solving proportions—statements that two ratios are equal. In this article, we’ll walk through how to solve the equation:

\[
\frac{3}{7} = \frac{9}{x}
\]

Understanding the Context

This equation presents a proportion where a fraction with numerator 3 and denominator 7 equals another fraction with numerator 9 and unknown denominator $ x $. Let’s break down the steps to find $ x $ and explain the logic behind it.

What Is a Proportion?

A proportion sets two fractions equal to each other, meaning the ratio on the left matches the ratio on the right. The equation:

\[
\frac{a}{b} = \frac{c}{d}
\]

$\frac { 9 x + 3 } { 9 } = 9 | Filo$

Image Gallery

$\frac { 9 x + 3 } { 9 } = 9 | Filo$

$Solved (e) By expressing \\( \\frac{9 x-17}{(4 x-7)(x-3)} | Chegg.com$

$Solved By expressing \$ \\frac{9 x-17}{(4 x-7)(x-3)} \$ in | Chegg.com$

$Find \( \lim \left(\frac{1}{3 x^{4 / | Chegg.com$

$`int_(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))\ dx` - YouTube$

Key Insights

can be solved by cross-multiplication, so long as $ b $ and $ d $ are not zero.

Step-by-Step Solution

Start with the given equation:

\[
\frac{3}{7} = \frac{9}{x}
\]

To eliminate denominators, cross-multiply:

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Final Thoughts

\[
3 \cdot x = 7 \cdot 9
\]

Simplify both sides:

\[
3x = 63
\]

Now divide both sides by 3 to isolate $ x $:

\[
x = \frac{63}{3} = 21
\]

Final Answer

\[
\boxed{x = 21}
\]

This means that when $ x = 21 $, the proportion $\frac{3}{7} = \frac{9}{21}$ holds true.

Why This Works: A Quick Check

Plug $ x = 21 $ back into the original proportion: