Math Problem Statement

The following table shows the steps involved in solving a linear equation. Which of the following properties correctly fills in the missing step used to get the equation in its corresponding form?

Solution

To determine the correct property for the missing step in the table, let's analyze the steps provided in the solution of the equation:

  1. Original Equation: 10=38x+210 = \frac{3}{8}x + 2
  2. Next Step (missing): 8=38x8 = \frac{3}{8}x

To go from 10=38x+210 = \frac{3}{8}x + 2 to 8=38x8 = \frac{3}{8}x, we would need to eliminate the constant term +2+2 from the right side. This is done by subtracting 2 from both sides of the equation. Thus, the missing step involves the Subtraction Property of Equality.

Therefore, the correct answer is:

Subtraction property of equality

Would you like further details on the solution steps or have any questions?

Here are some related questions that might help deepen your understanding:

  1. What is the Subtraction Property of Equality, and how is it applied in solving equations?
  2. How would the Addition Property of Equality be used in a similar equation?
  3. Can you describe the purpose of the Symmetric Property of Equality in solving equations?
  4. Why is it necessary to apply the Multiplication Property of Equality in some steps?
  5. How does solving this equation demonstrate the balance method in algebra?

Tip: Always remember to keep equations balanced by applying the same operation on both sides.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Properties of Equality

Formulas

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Theorems

Subtraction Property of Equality
Multiplication Property of Equality
Symmetric Property of Equality

Suitable Grade Level

Grades 6-8