Question

A student solves the following problem:
Problem: 2(x-3) + 3x = 19
Step 1: 2x6+3x = 19
Step 2: (2x+3x) - 6 = 19
Step 3: 5x6 = 19
Step 4: 5x6+6=19+6
Step 5: 5x 25
Step 6: x = 5
What property justifies step 4?

Answer 1

In step 4, the student is adding 6 to both sides of the equation \( 5x6 = 19 \) to isolate the term involving \( x \) on one side. The property that justifies this step is the **Addition Property of Equality**. This property states that if two quantities are equal, adding the same amount to both sides of the equation keeps them equal.

So, according to the Addition Property of Equality, if \( a = b \), then \( a + c = b + c \) for any real number \( c \). In this case, \( a \) is \( 5x6 \), \( b \) is 19, and \( c \) is 6.