Math Problem Statement
Suppose your friend says he can solve 3x = 15 using the Multiplication Property of Equality. Is he correct? Justify your response.
Solution
Yes, your friend is correct in using the Multiplication Property of Equality to solve the equation .
Justification:
The Multiplication Property of Equality states that if you multiply or divide both sides of an equation by the same non-zero number, the equality is preserved.
To solve , the goal is to isolate . You can do this by dividing both sides of the equation by 3 (the coefficient of ):
This simplifies to:
Therefore, your friend is correct because they are applying the Multiplication Property of Equality to isolate .
Would you like to go over any of these details? Here are some related questions to explore further:
- What is the Multiplication Property of Equality?
- How do you handle equations where the variable has a coefficient of zero?
- Can you apply this property to equations involving fractions?
- What if the equation was ? How would that affect the solution?
- How does this property differ from the Addition Property of Equality?
Tip: When solving linear equations, always check your solution by substituting it back into the original equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Multiplication Property of Equality
Formulas
3x = 15, x = 15/3
Theorems
Multiplication Property of Equality
Suitable Grade Level
Grades 6-8