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We are asked to find the value of \( x \) that makes the given statement true. The statement provided is:

\[
\frac{x - 5}{2x} = \frac{1}{3}
\]

This equation expresses that the ratio \( x - 5 \) to \( 2x \) is equivalent to the ratio \( 1 \) to \( 3 \).

### Steps to solve:

1. Start by cross-multiplying to eliminate the fractions:

\[
3(x - 5) = 1(2x)
\]

This simplifies to:

\[
3(x - 5) = 2x
\]

2. Expand the left-hand side:

\[
3x - 15 = 2x
\]

3. Now, solve for \( x \) by subtracting \( 2x \) from both sides:

\[
3x - 2x - 15 = 0
\]

Which simplifies to:

\[
x - 15 = 0
\]

4. Add 15 to both sides:

\[
x = 15
\]

Thus, the value of \( x \) is \( 15 \).

Would you like further explanation or details on any step? Here are 5 related questions you might find helpful:

1. How can you verify that \( x = 15 \) is the correct solution?
2. What would the ratio be if \( x = 10 \) instead of \( x = 15 \)?
3. What are some other common methods to solve ratios and proportions?
4. How do ratios change if the value of \( x \) increases or decreases?
5. Can this problem be solved graphically?

**Tip:** Always cross-check your solution by substituting it back into the original equation to ensure it satisfies the condition.

Work out the value of x that makes the statement below true. x - 5 : 2x is equivalent to 1 : 3.

Find the value of x for the equation where the ratio of (x - 5) to 2x is equal to 1 to 3. This problem involves cross-multiplication of proportions and solving linear equations, suitable for Grades 8-10.

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