A student solves the following problem:

Question

Problem:  2(x−3)+3x=19

Step 1:      2x−6+3x=19

Step2:      (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 step 4?

(1 point)
Responses

Substitution
Substitution

Commutative Property of Addition
Commutative Property of Addition

Multiplication Property of Equality
Multiplication Property of Equality

Addition Property of Equality

GPT-4o mini · Answer

The property that justifies step 4, where the student adds 6 to both sides of the equation to isolate the variable \( x \), is the Addition Property of Equality. This property states that if you add the same number to both sides of an equation, the two sides remain equal.

So, the correct response is:

Addition Property of Equality