Answer :
Certainly! Let's go through the given equation step by step, and identify the correct justification for each step, especially focusing on Step 2:
Given equation:
[tex]\[ 12y - 40 - 4y = 6y - 18 \][/tex]
Step 1: Combine like terms on the left side of the equation.
When combining like terms on the left side:
[tex]\[ 12y - 4y - 40 = 6y - 18 \][/tex]
Simplifies to:
[tex]\[ 8y - 40 = 6y - 18 \][/tex]
Step 2: Subtract \(6y\) from both sides of the equation.
To isolate the variable term involving \(y\):
[tex]\[ 8y - 40 - 6y = 6y - 18 - 6y \][/tex]
Simplifies to:
[tex]\[ 2y - 40 = -18 \][/tex]
The justification for subtracting \(6y\) from both sides of the equation to simplify it is based on the subtraction property of equality. This property states that you can subtract the same amount from both sides of an equation without changing the equality.
Therefore, the correct answer is:
[tex]\[ \boxed{D \text{. the subtraction property of equality}} \][/tex]
Given equation:
[tex]\[ 12y - 40 - 4y = 6y - 18 \][/tex]
Step 1: Combine like terms on the left side of the equation.
When combining like terms on the left side:
[tex]\[ 12y - 4y - 40 = 6y - 18 \][/tex]
Simplifies to:
[tex]\[ 8y - 40 = 6y - 18 \][/tex]
Step 2: Subtract \(6y\) from both sides of the equation.
To isolate the variable term involving \(y\):
[tex]\[ 8y - 40 - 6y = 6y - 18 - 6y \][/tex]
Simplifies to:
[tex]\[ 2y - 40 = -18 \][/tex]
The justification for subtracting \(6y\) from both sides of the equation to simplify it is based on the subtraction property of equality. This property states that you can subtract the same amount from both sides of an equation without changing the equality.
Therefore, the correct answer is:
[tex]\[ \boxed{D \text{. the subtraction property of equality}} \][/tex]
