Math Problem Statement
the sum of twice a number and 7 is the difference between the number and 2
Solution
Let's translate the problem into an equation:
Let the unknown number be .
- "Twice a number" translates to .
- "The sum of twice a number and 7" translates to .
- "The difference between the number and 2" translates to .
The equation based on the problem statement is:
Now, let's solve the equation:
- Subtract from both sides to get the terms involving on one side:
Simplifying:
- Subtract 7 from both sides to isolate :
Simplifying:
The solution is .
Would you like a detailed breakdown or have any questions?
Here are 5 related questions:
- What would the equation be if the sum was the product instead?
- How would the problem change if the 7 were replaced by another number?
- What is the solution if the sum of three times the number and 5 is the difference between the number and 3?
- How can we represent the problem graphically?
- What if the problem involved the square of the number instead of twice the number?
Tip: When solving equations, always aim to simplify the equation step by step, making sure to keep the equation balanced by performing the same operation on both sides.
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Math Problem Analysis
Mathematical Concepts
Equations
Algebra
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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