Expression I: 300x – (-75)Expression II: ___ + 300xWhat number should be placed in the blank to make Expression I equivalent to Expression II?
Question
Expression I: 300x – (-75)
Expression II: ___ + 300x
What number should be placed in the blank to make Expression I equivalent to Expression II?
Solution
1. Break Down the Problem
We need to find a number that can be placed in the blank of Expression II to make it equivalent to Expression I. The expressions are:
- Expression I:
- Expression II:
2. Relevant Concepts
To find the value of , we need to simplify Expression I and then set it equal to Expression II.
3. Analysis and Detail
Step 1: Simplify Expression I
Step 2: Set the Expressions Equal To find , we set the two expressions equal to each other:
Step 3: Solve for Subtract from both sides:
4. Verify and Summarize
Substituting back into Expression II: This matches Expression I since both simplify to .
Final Answer
The number that should be placed in the blank is .
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