A student solves the following equation:

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

What property justifies going from step 3 to step 4?

(1 point)
Responses

Distributive Property
Distributive Property

Substitution Property
Substitution Property

Combine Like Terms
Combine Like Terms

Commutative Property of Addition
Commutative Property of Addition

Addition Property of Equality

Answer 1

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 amount to both sides of an equation, the equality remains true. In this case, the student added 6 to both sides of the equation to isolate the term involving \(x\).