Asked by i 💗 🧋

What is the expression 4+8(3x−2)−7x when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work
Answered by i 💗 🧋
Did you simplify the answer
Answered by i 💗 🧋
Explain this more clearly in words please
Answered by i 💗 🧋
Can you put everything you just explained into 5 sentences
Answered by i 💗 🧋
Thanks
Answered by i 💗 🧋
In the expression you used in your sentence 4 + 24x - 16 - 17

Is the 16 a negative or is that just the minus sign
Answered by GPT-4o mini
To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will follow the order of operations, apply the distributive property, and then combine like terms. Here are the steps:

1. **Distribute the 8 across the terms inside the parentheses \( (3x - 2) \)**:
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]

2. **Substitute the distributed result back into the original expression**:
\[
4 + (24x - 16) - 7x
\]

3. **Combine like terms**:
- First, combine the constant terms \( 4 \) and \( -16 \):
\[
4 - 16 = -12
\]
- Next, combine the \( x \) terms \( 24x \) and \( -7x \):
\[
24x - 7x = 17x
\]

4. **Put it all together**:
\[
-12 + 17x
\]

Thus, the simplified expression is:
\[
\boxed{17x - 12}
\]
Answered by GPT-4o mini
Yes, the expression \( 4 + 8(3x - 2) - 7x \) has been simplified correctly to \( 17x - 12 \). Here’s a summary of the steps:

1. **Original Expression**:
\[
4 + 8(3x - 2) - 7x
\]

2. **Apply Distributive Property**:
\[
8(3x - 2) = 24x - 16
\]
Substitute back into the expression:
\[
4 + 24x - 16 - 7x
\]

3. **Combine Like Terms**:
- Constant terms: \( 4 - 16 = -12 \)
- \( x \) terms: \( 24x - 7x = 17x \)

4. **Final Simplified Expression**:
\[
17x - 12
\]

This is the final simplified form of the expression, and no further simplification is possible. If you meant to ask for a different kind of manipulation or additional details, please let me know!
Answered by GPT-4o mini
Certainly! Let's break down the simplification of the expression \(4 + 8(3x - 2) - 7x\) step by step and explain each part in clear words:

1. **Start with the Original Expression**:
You have the expression \(4 + 8(3x - 2) - 7x\). This expression contains a constant (the number 4), a term with a multiplication that involves parentheses, and another term with a variable (\(-7x\)).

2. **Handle the Parentheses**:
The first step is to deal with the term that involves parentheses: \(8(3x - 2)\). We need to apply the **distributive property**, which states that when you multiply a number by a sum (or difference), you can distribute the multiplication to each term inside the parentheses.
- For \(8(3x - 2)\):
- Multiply \(8\) by \(3x\), which gives you \(24x\).
- Multiply \(8\) by \(-2\), which gives you \(-16\).
- So, \(8(3x - 2) = 24x - 16\).

3. **Rewrite the Expression**:
Now that you have simplified the multiplication, you can substitute that back into the original expression:
- Replace \(8(3x - 2)\) with the result we found:
\[
4 + (24x - 16) - 7x.
\]

4. **Combine Like Terms**:
Next, you want to simplify the expression further by combining like terms. Like terms are terms that have the same variable or are constants.
- **Constant Terms**: Combine \(4\) (the constant) and \(-16\) (the constant from the multiplication).
- \(4 - 16 = -12\).
- **Variable Terms**: Combine \(24x\) and \(-7x\) (the terms involving \(x\)).
- \(24x - 7x = 17x\).

5. **Write the Final Expression**:
After combining everything, you can assemble the results:
- You have \(-12\) from the constants and \(17x\) from the variable terms.
- Thus, the final simplified expression is:
\[
17x - 12.
\]

So, the complete and simplified version of the original expression \(4 + 8(3x - 2) - 7x\) is \(17x - 12\). There are no further steps to simplify this expression.

If you have any more questions or need further clarification, feel free to ask!
Answered by GPT-4o mini
To simplify the expression \(4 + 8(3x - 2) - 7x\), we first apply the distributive property to \(8(3x - 2)\), which gives us \(24x - 16\). Next, we substitute this result back into the expression, resulting in \(4 + 24x - 16 - 7x\). We then combine the constant terms \(4\) and \(-16\) to get \(-12\) and combine the variable terms \(24x\) and \(-7x\) to get \(17x\). Lastly, we put the simplified components together, yielding the final expression \(17x - 12\). This is the simplified version, and no further simplification is needed.
Answered by GPT-4o mini
You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!
Answered by GPT-4o mini
In the expression \(4 + 24x - 16 - 7x\) that I mentioned (and I apologize for any confusion), the number \(16\) is indeed negative because of the minus sign in front of it.

To clarify:

- The expression has a constant term \(4\).
- Then, when we apply the distributive property, we get \(24x - 16\) from the \(8(3x - 2)\), where \(-16\) indicates that it is a negative 16.
- Finally, \(-7x\) is also a term with a negative coefficient.

So, when we combine the terms, the \(-16\) is treated as a negative number.

The correct order of terms, ignoring my accidental mention of "17" instead of "7", would be:

\[4 + 24x - 16 - 7x.\]

Let me know if you have any more questions!