To determine which justification correctly describes the process from Step 1 to Step 2, let's analyze the operations happening between these steps:
Step 1: [tex]\( 4x + 2 = 10 \)[/tex]
Step 2: [tex]\( 4x = 8 \)[/tex]
Between Step 1 and Step 2, we move from [tex]\( 4x + 2 = 10 \)[/tex] to [tex]\( 4x = 8 \)[/tex]. This transformation involves isolating the term with [tex]\( x \)[/tex] by removing the constant term [tex]\( 2 \)[/tex] on the left-hand side.
- Addition Property of Equality adds the same value to both sides of the equation.
- Subtraction Property of Equality subtracts the same value from both sides of the equation.
- Multiplication Property of Equality multiplies both sides of the equation by the same value.
- Division Property of Equality divides both sides of the equation by the same value.
By examining the steps, we know that to go from [tex]\( 4x + 2 = 10 \)[/tex] to [tex]\( 4x = 8 \)[/tex], we subtract 2 from both sides:
[tex]\[ 4x + 2 - 2 = 10 - 2 \][/tex]
[tex]\[ 4x = 8 \][/tex]
Thus, the correct justification is: "Using the subtraction property of equality, 2 is subtracted from both sides of the equation."
