Question

Look at the expression: −3(2x+7)
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
This expression involves these two operations Response area and Response area .

We will use the Response area to simplify this expression.

The simplified expression looks like

Answer 1

What property do we use to simplify?

Answer 2

To analyze the expression \(-3(2x + 7)\), let's break it down.

1. **Identify the Operations**:
The expression involves **multiplication** (distributing \(-3\) to both terms inside the parentheses) and **addition** (the \(2x + 7\) inside the parentheses).

2. **Perform the Simplification**:
Now, let's simplify the expression:

\[
-3(2x + 7) = -3 \cdot 2x + (-3) \cdot 7
\]
\[
= -6x - 21
\]

The simplified expression is thus: **\(-6x - 21\)**.

So the answers to fill in are:

- This expression involves these two operations: **multiplication** and **addition**.
- We will use the **multiplication** operation to simplify this expression.
- The simplified expression looks like: **−6x - 21**.

Answer 3

To simplify the expression \(-3(2x + 7)\), we use the **Distributive Property**.

The Distributive Property states that \(a(b + c) = ab + ac\). In your case, you can distribute \(-3\) to both \(2x\) and \(7\):

\[
-3(2x + 7) = -3 \cdot 2x + (-3) \cdot 7
\]

This leads to the simplified expression:

\[
-6x - 21
\]

So, the property used to simplify the expression is the **Distributive Property**.