Question

Solve the equation filling in the steps: 2(x−3)+21=−3

Distribute to get ____________________

Combine like terms to get ____________________

Use the (choose a property) ____________________ to get (resulting equation) ____________________

Use the (choose a property) ____________________ to get (resulting answer) ____________________

Answer 1

Let's solve the equation step by step. The given equation is:

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

### Step 1: Distribute to get
Distributing \( 2 \) inside the parentheses:

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

This simplifies to:

\[ 2x - 6 + 21 = -3 \]

So, the answer is:

**Distribute to get** \( 2x - 6 + 21 = -3 \).

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### Step 2: Combine like terms to get
Now, we combine the like terms \(-6\) and \(21\):

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

This simplifies to:

\[ 2x + 15 = -3 \]

So, the answer is:

**Combine like terms to get** \( 2x + 15 = -3 \).

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### Step 3: Use the (choose a property) to get (resulting equation)
Next, we want to isolate the term with \( x \) by using the **addition property of equality**. We subtract \( 15 \) from both sides:

\[ 2x + 15 - 15 = -3 - 15 \]

This results in:

\[ 2x = -18 \]

So, the answer is:

**Use the addition property of equality to get** \( 2x = -18 \).

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### Step 4: Use the (choose a property) to get (resulting answer)
Finally, we need to solve for \( x \) using the **multiplication property of equality** by dividing both sides by \( 2 \):

\[ \frac{2x}{2} = \frac{-18}{2} \]

This simplifies to:

\[ x = -9 \]

So, the answer is:

**Use the multiplication property of equality to get** \( x = -9 \).

In summary, we have:

1. **Distribute to get** \( 2x - 6 + 21 = -3 \).
2. **Combine like terms to get** \( 2x + 15 = -3 \).
3. **Use the addition property of equality to get** \( 2x = -18 \).
4. **Use the multiplication property of equality to get** \( x = -9 \).