The problem given asks which number Lucy should multiply both sides of the equation by to eliminate the fractions and generate an equivalent equation.

The equation shown in the image is:

$\frac{1}{2}x + \frac{3}{4} = \frac{3}{8}$

To eliminate the fractions:

1. Identify the denominators: The denominators in the equation are 2, 4, and 8.
2. Find the Least Common Denominator (LCD): The LCD of 2, 4, and 8 is 8.
3. Multiply the entire equation by the LCD: Multiplying both sides by 8 will eliminate the fractions.

Let's check the answer choices:

• A. 2: This won't eliminate all fractions.
• B. 4: This will not eliminate the $\frac{3}{8}$ term.
• C. 8: This is the correct choice since it will eliminate all fractions.
• D. 16: This is unnecessary and will result in larger numbers.

Conclusion:

Lucy should multiply both sides of the equation by 8 to eliminate the fractions and generate an equivalent equation.

Would you like further details or have any questions?

Related Questions:

1. What happens when you multiply each term by the LCD?
2. How can you verify if the new equation is equivalent to the original?
3. Why is it important to find the least common denominator?
4. What would happen if you multiplied by a number larger than the LCD?
5. Can this method be used for equations with variables in the denominator?

Tip:

Always simplify fractions first to make solving equations easier.