To solve the problem, we need to identify which of the given options (A, B, C, or D) is equivalent to the expression $ 3(x + 4) $. Let's break it down step by step.
Step 1: Understand the Problem
We are tasked with finding an expression that is equivalent to $ 3(x + 4) $. This involves distributing the 3 across the terms inside the parentheses.
Step 2: Distribute the 3
The distributive property states that:
$$
a(b + c) = ab + ac
$$
Applying this to $ 3(x + 4) $:
$$
3(x + 4) = 3 \cdot x + 3 \cdot 4
$$
Simplify the multiplication:
$$
3(x + 4) = 3x + 12
$$
Step 3: Compare with the Given Options
Now, let's compare $ 3x + 12 $ with the options provided:
-
Option A: $ 3x + 4 $
-
Option B: $ 3x + 12 $
-
Option C: $ 3x - 12 $
-
Option D: $ 3x + 7 $
From the comparison, we see that:
$$
3(x + 4) = 3x + 12
$$
This matches
Option B.
Step 4: Verify the Answer
To ensure accuracy, let's verify by substituting a value for $ x $. For example, let $ x = 2 $:
- Original expression: $ 3(x + 4) = 3(2 + 4) = 3 \cdot 6 = 18 $
- Option B: $ 3x + 12 = 3(2) + 12 = 6 + 12 = 18 $
Both give the same result, confirming that
Option B is correct.
Final Answer:
$$
\boxed{B}
$$
Parent Tip: Review the logic above to help your child master the concept of math translation worksheet.
