Math Problem Statement
Solution
In the image, the balance scale represents an equation. Let's break down the model and translate it into a mathematical equation:
Left Side of the Scale:
- There are 2 blocks labeled "x" and 3 single units (which represent +3).
Right Side of the Scale:
- There is 1 block labeled "x" and 3 single units (which represent +3).
Equation Setup:
Based on the balance scale, the total weight on both sides must be equal, so the equation represented by this model can be written as:
Simplifying the Equation:
We can simplify this equation by subtracting and 3 from both sides:
-
Subtract 3 from both sides:
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Subtract from both sides:
Conclusion:
The value of is 0. Therefore, the correct answer to Part 2 is D: .
Would you like further clarification on this solution or any other details?
Here are 5 related questions to deepen your understanding:
- What happens if we change the number of single units on either side?
- How would the equation change if there were 3 blocks of on the right side?
- Can you solve the equation by adding different values of first?
- What type of equations can be represented using this balance model?
- How does subtracting or adding equal values to both sides affect the balance?
Tip: Always isolate the variable step by step to simplify solving the equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Balancing Equations
Formulas
Equation of balance scale: 2x + 3 = x + 3
Theorems
Equality Theorem
Linear Equation Simplification
Suitable Grade Level
Grades 6-8