To determine which of the given expressions are equivalent to the algebraic expression \((2x−1)−3.25(x+3)\), we first need to simplify the original expression.
Starting with:
\[ (2x−1)−3.25(x+3) \]
Distribute the \(-3.25\) across \((x + 3)\):
\[ (2x - 1) - (3.25x + 9.75) \]
Now combine like terms:
\[ 2x - 1 - 3.25x - 9.75 \]
Combine the \(x\) terms and the constant terms:
\[ (2x - 3.25x) + (-1 - 9.75) \]
This simplifies to:
\[ -1.25x - 10.75 \]
Now, we need to check which of the provided options are equivalent to \(-1.25x - 10.75\):
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\(2x−1−3.25x−9.75\): This simplifies to \(-1.25x - 10.75\). (Equivalent)
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\(2x−3.25x−1−9.75\): This also simplifies to \(-1.25x - 10.75\). (Equivalent)
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\(−1.25x−1−9.75\): This simplifies to \(-1.25x - 10.75\). (Equivalent)
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\(−1.25x−10.75\): This is exactly the same as \(-1.25x - 10.75\). (Equivalent)
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\(2x−1−3.25x+9.75\): This simplifies to \(-1.25x + 8.75\). (Not Equivalent)
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\(1.25x + 10.75\): This is \(1.25x + 10.75\). (Not Equivalent)
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\(−1.25x−4\): This simplifies to \(-1.25x - 4\). (Not Equivalent)
So, the equivalent expressions are:
- \(2x−1−3.25x−9.75\)
- \(2x−3.25x−1−9.75\)
- \(−1.25x−1−9.75\)
- \(−1.25x−10.75\)
Thus, the correct responses are:
- \(2x−1−3.25x−9.75\)
- \(2x−3.25x−1−9.75\)
- \(−1.25x−1−9.75\)
- \(−1.25x−10.75\)