Question

A student solves the following equation:

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?

What property justifies going from step 3 to step 4?

(1 point)
Responses

Commutative Property of Addition
Commutative Property of Addition

Combine Like Terms
Combine Like Terms

Distributive Property
Distributive Property

Substitution Property
Substitution Property

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 number to both sides of an equation, the equation remains balanced. In this case, 6 is added to both sides of the equation \(5x - 6 = 19\) to yield \(5x = 25\).