Question

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


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

I don't see that option for step 4, what is another way to say the 4th step?

Answer 2

I don't see 2x = -3 - 15

Answer 3

I mean for step 3, what is another way to say step 3?

Answer 4

That is step 2, not 3

Answer 5

Let's solve the equation step by step:

1. **Original equation**:

\[
2(x−3)+21=−3
\]

2. **Distribute** to get:

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

(Here, \(2\) is multiplied by both \(x\) and \(-3\).)

3. **Combine like terms** to get:

\[
2x + 15 = -3
\]

(The \(-6\) and \(21\) combine to \(15\).)

4. **Use the subtraction property of equality** to get:

\[
2x = -3 - 15
\]

(We subtract \(15\) from both sides of the equation.)

5. **Combine** to get:

\[
2x = -18
\]

6. **Use the division property of equality** to get:

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

(We divide both sides by \(2\).)

7. **Simplify** to get:

\[
x = -9
\]

So, the solution to the equation is \(x = -9\).

To summarize:
- Distribute to get: \(2x - 6 + 21 = -3\)
- Combine like terms to get: \(2x + 15 = -3\)
- Use the subtraction property of equality to get: \(2x = -3 - 15\)
- Use the division property of equality to get: \(x = -9\)

Answer 6

Absolutely! For step 4, instead of saying "Use the subtraction property of equality," you can say:

**Use the additive inverse property** to get:

\[
2x = -3 - 15
\]

The additive inverse property emphasizes that to isolate \(x\), we are effectively "removing" \(15\) from the left side by adding its opposite, which is \(-15\).

So, the revised step could be:

4. **Use the additive inverse property** to get:

\[
2x = -3 - 15
\]

Thank you for pointing that out!

Answer 7

I apologize for the confusion in the explanation. Let's clarify and rewrite that step correctly.

After combining like terms, we had:

\[
2x + 15 = -3
\]

When isolating \(2x\), you subtract \(15\) from both sides of the equation. Let's rewrite step 4 clearly and correctly:

4. **Use the additive inverse property** to get:

\[
2x = -3 - 15
\]

This is correct. Now combining the right-hand side:

\[
2x = -18
\]

So indeed, **after subtracting \(15\)** from both sides, we correctly reach \(2x = -18\).

To summarize the steps one more time:

1. **Original equation**:
\[
2(x−3)+21=−3
\]

2. **Distribute**:
\[
2x - 6 + 21 = -3
\]

3. **Combine like terms**:
\[
2x + 15 = -3
\]

4. **Use the additive inverse property** to isolate \(2x\):
\[
2x = -3 - 15
\]

5. **Combine**:
\[
2x = -18
\]

6. **Use the division property of equality**:
\[
x = \frac{-18}{2}
\]

7. **Simplify**:
\[
x = -9
\]

Your final answer is \(x = -9\). Thank you for your patience, and I hope this clears up any confusion!

Answer 8

For step 3, instead of saying "Combine like terms," you could say:

**Simplify the left side** to get:

This highlights the action of combining the constants directly without specifically labeling them as "like terms."

So, step 3 would then be rewritten as:

3. **Simplify the left side** to get:

\[
2x + 15 = -3
\]

Thank you for your feedback, and I'm glad to provide alternative phrasing!

Answer 9

I apologize for the mix-up. Let's clarify step 3 correctly. After you have distributed and simplified the left side in step 2, you have:

\[
2x + 15 = -3
\]

Now for step 3, instead of saying "Combine like terms," you can say:

**Move the constant to the right side** to get:

\[
2x = -3 - 15
\]

So the revised step 3 could be phrased as:

3. **Move the constant to the right side** to get:

\[
2x = -3 - 15
\]

Thank you for your patience as we clarify these steps!