Answer :
To determine which property justifies the statement "If [tex]\( 3x + 14 = 80 \)[/tex], then [tex]\( 3x = 66 \)[/tex]," let's examine the steps involved in transforming the given equation:
1. The initial equation is:
[tex]\[ 3x + 14 = 80 \][/tex]
2. To simplify this equation and isolate the term involving [tex]\( x \)[/tex], we need to remove the constant term [tex]\( 14 \)[/tex] from the left side. This can be achieved by subtracting [tex]\( 14 \)[/tex] from both sides of the equation.
3. Performing the subtraction on both sides, we get:
[tex]\[ 3x + 14 - 14 = 80 - 14 \][/tex]
4. Simplifying both sides results in:
[tex]\[ 3x = 66 \][/tex]
The property used in this step is the Subtraction Property of Equality. This property states that if you subtract the same amount from both sides of an equation, the two sides remain equal.
Therefore, the correct answer is:
D. Subtraction Property of Equality
1. The initial equation is:
[tex]\[ 3x + 14 = 80 \][/tex]
2. To simplify this equation and isolate the term involving [tex]\( x \)[/tex], we need to remove the constant term [tex]\( 14 \)[/tex] from the left side. This can be achieved by subtracting [tex]\( 14 \)[/tex] from both sides of the equation.
3. Performing the subtraction on both sides, we get:
[tex]\[ 3x + 14 - 14 = 80 - 14 \][/tex]
4. Simplifying both sides results in:
[tex]\[ 3x = 66 \][/tex]
The property used in this step is the Subtraction Property of Equality. This property states that if you subtract the same amount from both sides of an equation, the two sides remain equal.
Therefore, the correct answer is:
D. Subtraction Property of Equality
