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) _____________
Fill In The Blanks
Options: Subtraction Property of Equality, x = 24, x = - 21/2, Division Property of Equality, 2x + 18 = -3, Addition Property of Equality, x = -9, 2x - 3 + 21 = -3, 2x = -21, 2x + 15 = -3, 2x = -18, -1x = -24, 2x - 6 + 21 = -3, Multiplication Property of Equality

Answer 1

are you sure these answers are correct

Answer 2

Let's solve the equation step by step, filling in the blanks.

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

2. **Combine like terms to get**:
Combining \(-6\) and \(21\) gives:
\( 2x + 15 = -3 \)

3. **Use the (choose a property)**:
We will use the **Subtraction Property of Equality** to isolate \(2x\):
Subtract \(15\) from both sides:
\( 2x + 15 - 15 = -3 - 15 \)
Resulting equation:
\( 2x = -18 \)

4. **Use the (choose a property)**:
Now we will use the **Division Property of Equality** to solve for \(x\):
Divide both sides by \(2\):
\( x = \frac{-18}{2} \)
Resulting answer:
\( x = -9 \)

So, the completed solution is:
1. Distribute to get **2x - 6 + 21 = -3**
2. Combine like terms to get **2x + 15 = -3**
3. Use the (choose a property) **Subtraction Property of Equality** to get (resulting equation) **2x = -18**
4. Use the (choose a property) **Division Property of Equality** to get (resulting answer) **x = -9**.

Answer 3

Yes, let's verify the solution step by step to ensure everything is correct.

The original equation is:

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

1. **Distribute to get**:
We need to distribute \(2\) into \((x - 3)\):
\[
2 \cdot x - 2 \cdot 3 + 21 = -3
\]
This simplifies to:
\[
2x - 6 + 21 = -3
\]

2. **Combine like terms to get**:
Combine the constants \(-6\) and \(21\):
\[
2x + 15 = -3
\]

3. **Use the (choose a property)**:
To isolate \(2x\), we will use the **Subtraction Property of Equality**. Subtract \(15\) from both sides:
\[
2x + 15 - 15 = -3 - 15
\]
Resulting in:
\[
2x = -18
\]

4. **Use the (choose a property)**:
To solve for \(x\), we will use the **Division Property of Equality**. Divide both sides by \(2\):
\[
x = \frac{-18}{2}
\]
Which simplifies to:
\[
x = -9
\]

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

To summarize:
1. Distribute to get **2x - 6 + 21 = -3**
2. Combine like terms to get **2x + 15 = -3**
3. Use the (choose a property) **Subtraction Property of Equality** to get (resulting equation) **2x = -18**
4. Use the (choose a property) **Division Property of Equality** to get (resulting answer) **x = -9**.

These steps and answers are verified to be accurate.