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To solve the equation \( \frac{x - 3}{4} = \frac{x}{10} \), we will follow these steps:

### Step 1: Eliminate the denominators.
To eliminate the denominators, multiply both sides of the equation by the least common denominator (LCD) of 4 and 10, which is 20.

\[
20 \cdot \frac{x - 3}{4} = 20 \cdot \frac{x}{10}
\]

Simplifying both sides:

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

### Step 2: Distribute and solve for \(x\).
Now, distribute the 5 on the left side:

\[
5x - 15 = 2x
\]

### Step 3: Isolate \(x\).
Move all terms involving \(x\) to one side of the equation:

\[
5x - 2x = 15
\]

Simplify:

\[
3x = 15
\]

### Step 4: Solve for \(x\).

\[
x = \frac{15}{3} = 5
\]

Thus, the value of \(x\) is **5**. The correct answer is option 2.

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Do you want more details or have any questions?

Here are 5 related questions you can explore:
1. How would the solution change if the constants in the equation were different?
2. What happens if the denominators were already the same in the original equation?
3. Can you solve for \(x\) if the equation was \( \frac{x - 3}{4} = \frac{x + 1}{10} \)?
4. How would the problem change if fractions were replaced by decimals?
5. How can we graphically represent the equation \( \frac{x - 3}{4} = \frac{x}{10} \)?

**Tip:** Always check for the least common denominator when solving equations involving fractions—it simplifies the process.

Learn how to solve the equation (x - 3)/4 = x/10 with a step-by-step approach. This example demonstrates core algebraic techniques like cross-multiplication and using the distributive property. Perfect for Grades 7-9.

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