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 3x=153x = 15.

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 3x=153x = 15, the goal is to isolate xx. You can do this by dividing both sides of the equation by 3 (the coefficient of xx):

3x3=153\frac{3x}{3} = \frac{15}{3}

This simplifies to:

x=5x = 5

Therefore, your friend is correct because they are applying the Multiplication Property of Equality to isolate xx.


Would you like to go over any of these details? Here are some related questions to explore further:

  1. What is the Multiplication Property of Equality?
  2. How do you handle equations where the variable has a coefficient of zero?
  3. Can you apply this property to equations involving fractions?
  4. What if the equation was 3x=153x = -15? How would that affect the solution?
  5. 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