Let's walk through the steps Simonne used to simplify the expression and understand the property of real numbers that was used:
Given the expression:
[tex]\[ 12 - 3(-2x + 4) \][/tex]
### Step 1: Distribute [tex]\(-3\)[/tex] inside the parentheses
[tex]\[ 12 + (-3)(-2x) + (-3)(4) \][/tex]
Here, the distributive property was used to remove the parentheses.
### Step 2: Simplify the multiplications
[tex]\[ 12 + 6x + (-12) \][/tex]
Since [tex]\((-3) \cdot (-2x) = 6x\)[/tex] and [tex]\((-3) \cdot 4 = -12\)[/tex], we perform the multiplications.
### Step 3: Combine like terms
[tex]\[ 12 + (-12) + 6x \][/tex]
At this stage, we see the terms [tex]\(12\)[/tex] and [tex]\(-12\)[/tex] can be combined.
### Step 4: Simplify [tex]\(12 + (-12)\)[/tex] to 0
[tex]\[ 0 + 6x \][/tex]
Here, we used the inverse property of addition, which states that any number added to its negative (inverse) results in 0. Hence, [tex]\(12 + (-12) = 0\)[/tex].
### Step 5: Simplify the expression further
[tex]\[ 6x \][/tex]
Since [tex]\(0 + 6x\)[/tex] is simply [tex]\(6x\)[/tex], we arrive at the final simplified form.
Thus, the property of real numbers used to transition from Step 3 to Step 4 is the:
[tex]\[ \boxed{\text{inverse property of addition}} \][/tex]
