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Answer:
To find expressions equivalent to \( 4x + 2 - (5x - 1) \), let's simplify the given expression:
\[ 4x + 2 - (5x - 1) \]
Distribute the negative sign through the parentheses:
\[ 4x + 2 - 5x + 1 \]
Combine like terms:
\[ (4x - 5x) + (2 + 1) \]
\[ -x + 3 \]
Now, let's evaluate each provided expression to see if it matches \(-x + 3\):
1. \( 4x + 2 + (-5x) - (-1) \)
Simplify inside the parentheses:
\[ 4x + 2 - 5x + 1 \]
Combine like terms:
\[ -x + 3 \]
This expression is equivalent to \(-x + 3\).
2. \( 4x + 2 - 5x - 1 \)
Simplify inside the parentheses:
\[ 4x - 5x + 2 - 1 \]
Combine like terms:
\[ -x + 1 \]
This expression is not equivalent to \(-x + 3\).
3. \( 4x - 5x + 2 - 1 \)
Combine like terms:
\[ -x + 1 \]
This expression is not equivalent to \(-x + 3\).
4. \(-x + 3\)
This expression is already in the simplified form and is equivalent to \(-x + 3\).
5. \( 4x + (-5x) + 2 + 1 \)
Simplify inside the parentheses:
\[ 4x - 5x + 2 + 1 \]
Combine like terms:
\[ -x + 3 \]
This expression is equivalent to \(-x + 3\).
So, the expressions that are equivalent to \( 4x + 2 - (5x - 1) \) are:
- \( 4x + 2 + (-5x) - (-1) \)
- \(-x + 3\)
- \( 4x + (-5x) + 2 + 1 \)