Question
POSSIBLE POINTS: 3.45
A student solves the following problem:
Problem:
2(x−3) + 3x = 19
Step 1: 2x − 6 + 3x = 19 Click and drag to move
Step2: (2x + 3x) −6 = 19 Click and drag to move
Step 3: 5x − 6 = 19 Click and drag to move
Step 4: 5x - 6 + 6 = 19 + 6 Click and drag to move
Step 5: 5x = 25 Click and drag to move
Step 6: x = 5 Click and drag to move
What property justifies going from step 3 to step 4?
Responses
A student solves the following problem:
Problem:
2(x−3) + 3x = 19
Step 1: 2x − 6 + 3x = 19 Click and drag to move
Step2: (2x + 3x) −6 = 19 Click and drag to move
Step 3: 5x − 6 = 19 Click and drag to move
Step 4: 5x - 6 + 6 = 19 + 6 Click and drag to move
Step 5: 5x = 25 Click and drag to move
Step 6: x = 5 Click and drag to move
What property justifies going from step 3 to step 4?
Responses
Answers
GPT-4o mini
The property that justifies going from step 3 to step 4 is the **Addition Property of Equality**.
This property states that if you add the same value to both sides of an equation, the two sides remain equal. In this case, adding 6 to both sides of the equation \(5x - 6 = 19\) to get \(5x = 25\) demonstrates this property.
This property states that if you add the same value to both sides of an equation, the two sides remain equal. In this case, adding 6 to both sides of the equation \(5x - 6 = 19\) to get \(5x = 25\) demonstrates this property.