Expression I: 300x – (-75)Expression II: ___ + 300xWhat number should be placed in the blank to make Expression I equivalent to Expression II?

1. Break Down the Problem

We need to find a number $y$ that can be placed in the blank of Expression II to make it equivalent to Expression I. The expressions are:

• Expression I: $300x - (-75)$
• Expression II: $y + 300x$

2. Relevant Concepts

To find the value of $y$, we need to simplify Expression I and then set it equal to Expression II.

3. Analysis and Detail

Step 1: Simplify Expression I $300x - (-75) = 300x + 75$

Step 2: Set the Expressions Equal To find $y$, we set the two expressions equal to each other: $300x + 75 = y + 300x$

Step 3: Solve for $y$ Subtract $300x$ from both sides: $75 = y$

4. Verify and Summarize

Substituting $75$ back into Expression II: $y + 300x = 75 + 300x$ This matches Expression I since both simplify to $300x + 75$.

Final Answer

The number that should be placed in the blank is $75$.