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Let's solve the equation \( 5(x + bd) = 2(x + ac) \) and make \( x \) the subject.

### Step-by-step solution:
1. Expand both sides of the equation:
   \[
   5(x + bd) = 5x + 5bd
   \]
   \[
   2(x + ac) = 2x + 2ac
   \]

2. Now, write the equation with both expansions:
   \[
   5x + 5bd = 2x + 2ac
   \]

3. Get all terms with \( x \) on one side and constants on the other:
   \[
   5x - 2x = 2ac - 5bd
   \]
   \[
   3x = 2ac - 5bd
   \]

4. Finally, divide both sides by 3 to isolate \( x \):
   \[
   x = \frac{2ac - 5bd}{3}
   \]

### Answer:
The correct choice is:
\[
\boxed{\text{c. } x = \frac{2ac - 5bd}{3}}
\]

Would you like further explanation or more details?

Here are five relative questions:
1. How do you solve similar equations with two variables?
2. What are some common techniques to isolate variables in equations?
3. How can you check if your solution for \( x \) is correct?
4. What are the applications of making a variable the subject in equations?
5. How would the equation change if it was \( 5(x + bd) = 3(x + ac) \)?

**Tip:** Always check your final equation by plugging the solution back into the original to ensure correctness.

Make x the subject for the following formula: 5(x + bd) = 2(x + ac).

Learn how to solve for x in the equation 5(x + bd) = 2(x + ac). This step-by-step algebraic solution uses basic algebra techniques such as the distributive property and variable isolation, suitable for students in Grades 9-11.

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