A student solves the following problem:

Question

Problem: 2(x - 3) + 3x = 19
Step 1: 2x - 6 + 3x = 19
Step 2: (2x + 3x) - 6 = 19
Step 3: 5x - 6 = 19
Step 4: 5x - 6 + 6 = 19 + 6
Step 5: 5x = 25
Step 6: x = 5
A) Multiplication Property of Equality
B) Commutative Property of Addition
C) Addition Property of Equality
D) Substitution

Answer 1

Let's analyze the steps taken by the student to determine which property applies to each step:

1. Step 1: \(2(x - 3) + 3x = 19\) simplifies to \(2x - 6 + 3x = 19\). This step involves distributing \(2\) to both \(x\) and \(-3\), and does not explicitly apply any of the properties listed.

2. Step 2: Rearranged to \((2x + 3x) - 6 = 19\). This step is using the Commutative Property of Addition, as the student is regrouping the terms.

3. Step 3: \(5x - 6 = 19\). This is just a simplification of the expression from Step 2 and doesn't explicitly invoke any property.

4. Step 4: \(5x - 6 + 6 = 19 + 6\). This step applies the Addition Property of Equality, as the same value (6) is added to both sides of the equation.

5. Step 5: \(5x = 25\). This is again a simplification step, arising from Step 4.

6. Step 6: \(x = 5\). This step involves the division operation, which is generally influenced by the properties of equality as well.

From the options given for the step where addition was applied to both sides (specifically in Step 4), the correct answer is:

C) Addition Property of Equality.