Question

. Solve the equation filling in the steps: 2(x−3)+21=−3
(6 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.
Distribute to get Response area

Combine like terms to get Response area

Use the (choose a property) Response area to get (resulting equation) Response area

Use the (choose a property) Response area to get (resulting answer) Response area

Answer 1

Let's solve the equation step by step.

Given the equation:
\[ 2(x - 3) + 21 = -3 \]

**Step 1: Distribute to get Response area**
We will distribute the \(2\) in the left-hand side:
\[ 2 \cdot x - 2 \cdot 3 + 21 = -3 \]
This simplifies to:
\[ 2x - 6 + 21 = -3 \]

**Response area:** \(2x - 6 + 21 = -3\)

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**Step 2: Combine like terms to get Response area**
Now, we combine the like terms \(-6\) and \(21\):
\[ 2x + 15 = -3 \]

**Response area:** \(2x + 15 = -3\)

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**Step 3: Use the (choose a property) Response area to get (resulting equation) Response area**
Next, we will use the **Subtraction Property** to isolate \(2x\) by subtracting \(15\) from both sides:
\[ 2x + 15 - 15 = -3 - 15 \]
This simplifies to:
\[ 2x = -18 \]

**Response area:** \(2x = -18\)

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**Step 4: Use the (choose a property) Response area to get (resulting answer) Response area**
Now, we will use the **Division Property** to solve for \(x\) by dividing both sides by \(2\):
\[ x = \frac{-18}{2} \]
This simplifies to:
\[ x = -9 \]

**Response area:** \(x = -9\)

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So, the final answer is \( x = -9 \).