Ask a New Question
Menu

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

11 answers

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: \[ \boxed{17x - 12} \]

Did you simplify the answer

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!

Explain this more clearly in words please

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!

Can you put everything you just explained into 5 sentences

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.

Thanks

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!

In the expression you used in your sentence 4 + 24x - 16 - 17

Is the 16 a negative or is that just the minus sign

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!