Question
What is the algebraic expression that is equivalent to (3x+2)−2.5(x−4)? Select all that apply. Explain your answer.
Answers
GPT-4o mini
To find an algebraic expression equivalent to \( (3x + 2) - 2.5(x - 4) \), we need to simplify it. Let's break it down step-by-step:
1. **Distribute \( -2.5 \)** across \( (x - 4) \):
\[
-2.5(x - 4) = -2.5x + 10
\]
2. **Substitute back into the original expression**:
\[
(3x + 2) - 2.5(x - 4) = (3x + 2) + (-2.5x + 10)
\]
3. **Combine like terms**:
\[
3x - 2.5x + 2 + 10 = (3 - 2.5)x + (2 + 10) = 0.5x + 12
\]
Thus, the simplified expression is:
\[
0.5x + 12
\]
Therefore, any algebraic expression equivalent to this simplified form \( 0.5x + 12 \) would also be correct.
**Explanation**:
- We expanded and combined like terms, showing that the original expression simplifies to \( 0.5x + 12 \).
- Equivalent expressions can be formed through different methods (factoring, distributing, etc.), but they ultimately give the same value for all allowed values of \( x \).
If you have other options listed, check if they simplify to \( 0.5x + 12 \) or any form that is mathematically equivalent (like converting to fractions or combining further).
The answer will be the expressions that equal \( 0.5x + 12 \) or are transformed versions of it (such as \( \frac{1}{2}x + 12 \), etc.).
1. **Distribute \( -2.5 \)** across \( (x - 4) \):
\[
-2.5(x - 4) = -2.5x + 10
\]
2. **Substitute back into the original expression**:
\[
(3x + 2) - 2.5(x - 4) = (3x + 2) + (-2.5x + 10)
\]
3. **Combine like terms**:
\[
3x - 2.5x + 2 + 10 = (3 - 2.5)x + (2 + 10) = 0.5x + 12
\]
Thus, the simplified expression is:
\[
0.5x + 12
\]
Therefore, any algebraic expression equivalent to this simplified form \( 0.5x + 12 \) would also be correct.
**Explanation**:
- We expanded and combined like terms, showing that the original expression simplifies to \( 0.5x + 12 \).
- Equivalent expressions can be formed through different methods (factoring, distributing, etc.), but they ultimately give the same value for all allowed values of \( x \).
If you have other options listed, check if they simplify to \( 0.5x + 12 \) or any form that is mathematically equivalent (like converting to fractions or combining further).
The answer will be the expressions that equal \( 0.5x + 12 \) or are transformed versions of it (such as \( \frac{1}{2}x + 12 \), etc.).