Question

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

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

The option "Division Property of Equality" (7 of 14) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Answer 1

Let's solve the equation step by step:

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

### Step 1: Distribute
We need to distribute the 2 across the terms inside the parentheses.
\[
2(x) - 2(3) + 21 = -3
\]
This simplifies to:
\[
2x - 6 + 21 = -3
\]

### Step 2: Combine like terms
Now, combine like terms on the left side:
\[
2x + ( -6 + 21 ) = -3
\]
This simplifies to:
\[
2x + 15 = -3
\]

### Step 3: Use the Subtraction Property of Equality
To isolate the term with x, we subtract 15 from both sides:
\[
2x + 15 - 15 = -3 - 15
\]
This results in:
\[
2x = -18
\]

### Step 4: Use the Division Property of Equality
Next, we divide both sides by 2 to solve for x:
\[
\frac{2x}{2} = \frac{-18}{2}
\]
This simplifies to:
\[
x = -9
\]

### Final Answer
The solution to the equation is:
\[
x = -9
\]