Math Problem Statement
Fill in the table to determine the ending and starting numbers by working backward through the mathematical operations.
Solution
I see you've uploaded an image that involves working backward through a problem with a table and equations. Let me analyze and break down the steps for solving it:
Table Analysis:
The table has four columns:
- Starting value
- Multiply by 7 (resulting in )
- Add 10 (resulting in )
- Multiply by 2 (resulting in )
We are tasked to:
- Fill in missing values in the table based on the operations.
- Use the given values (e.g., starting at or ending at ) to work backward where necessary.
Step-by-Step Solution:
First Row:
- Starting value:
- Multiply by 7:
- Add 10:
- Multiply by 2:
Since we are working symbolically, this row is already complete.
Second Row:
- Starting value:
Steps:
- Multiply by 7:
- Add 10:
- Multiply by 2:
Complete row:
- Multiply by 7:
- Add 10:
- Multiply by 2:
Third Row:
- The final value is .
We need to work backward:
- Divide by 2 (reverse of multiplying by 2):
- Subtract 10 (reverse of adding 10):
- Divide by 7 (reverse of multiplying by 7):
Complete row:
- Starting value:
- Multiply by 7:
- Add 10:
- Multiply by 2:
Completed Table:
Starting | Multiply by 7 | Add 10 | Multiply by 2 |
---|---|---|---|
Would you like further explanation of any specific step, or help with similar problems?
Related Questions:
- How do you reverse each operation in an equation?
- Why is dividing the last value by 2 the first step when working backward?
- How can you generalize this process for any function or equation?
- What is the importance of inverse operations in solving equations?
- Can you create a similar problem using different operations?
Tip:
Always apply inverse operations in reverse order when working backward to ensure accuracy!
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Math Problem Analysis
Mathematical Concepts
Algebra
Inverse Operations
Equations
Formulas
y = 7x
y = 7x + 10
y = 2(7x + 10)
Theorems
Inverse Operations Principle
Suitable Grade Level
Grades 6-8