https://file.aiquickdraw.com/mathbot/file/1725491988546w5xpbk0f.jpg

The problem shown in the image involves solving the equation:

\[
\frac{1}{2}x - \frac{3}{4} = \frac{3}{8}
\]

The question asks what number should be chosen to multiply both sides of the equation in order to generate an equivalent equation for solving it.

### Solution Approach:
To eliminate the fractions, we need to find a common denominator. The denominators in the equation are 2, 4, and 8. The least common denominator (LCD) of 2, 4, and 8 is 8. Thus, multiplying the entire equation by 8 will eliminate the fractions.

Let's see the options:

- A. 2
- B. 4
- C. 8
- D. 16

### Correct Answer:
Multiplying by 8 would eliminate all fractions in the equation, so **C. 8** is the correct answer.

Would you like more details or have any questions?

Here are 5 related questions:
1. What happens to each term when you multiply by 8 in this case?
2. How do you determine the least common denominator?
3. Can you explain how to solve for \( x \) after eliminating the fractions?
4. What if the denominators were different? How would the solution change?
5. How can you check that your solution to the equation is correct?

**Tip:** Always look for the least common denominator when trying to eliminate fractions from an equation.

Lucy is working with her partner to solve the equation \( \frac{1}{2}x - \frac{3}{4} = \frac{3}{8} \). What number should Lucy choose to multiply both sides of the equation to generate an equivalent equation in order to solve?

Understand how to solve the equation \( \frac{1}{2}x - \frac{3}{4} = \frac{3}{8} \) by multiplying both sides by 8 to eliminate fractions. This problem is ideal for students in Grades 7-8 learning algebraic methods for solving equations involving fractions.

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