Question

A student solves the following problem: Problem: 2(x−3)+3x=192(x−3)+3x=19 Step 1: 2x−6+3x=192x−6+3x=19 Step 2: (2x+3x)−6=19(2x+3x)−6=19 Step 3: 5x−6=195x−6=19 Step 4: 5x−6+6=19+65x−6+6=19+6 Step 5: 5x=255x=25 Step 6: x=5x=5 What property justifies step 4? (1 point) Responses Substitution Substitution Commutative Property of Addition Commutative Property of Addition Addition Property of Equality Addition Property of Equality Multiplication Property of Equality

Answer 1

The property that justifies step 4, where \( 5x - 6 + 6 = 19 + 6 \), 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, adding 6 to both sides maintains the equality between \( 5x - 6 \) and \( 19 \).