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? (1 point) Responses Commutative Property of Addition Commutative Property of Addition Substitution Property Substitution Property Combine Like Terms Combine Like Terms Distributive Property Distributive 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 quantity 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) allows the equation to maintain its equality while isolating the term with \( x \).