To determine which expressions are equivalent to \((2x - 1) - 3.25(x + 3)\), we'll first simplify the original expression step by step.
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Expand the second term: \[ 3.25(x + 3) = 3.25x + 9.75 \]
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Substitute this back into the expression: \[ (2x - 1) - (3.25x + 9.75) \]
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Distribute the negative sign: \[ 2x - 1 - 3.25x - 9.75 \]
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Combine like terms:
- The \(x\) terms: \(2x - 3.25x = -1.25x\)
- The constant terms: \(-1 - 9.75 = -10.75\)
This gives us the simplified expression: \[ -1.25x - 10.75 \]
Now, let's compare this result with the given responses to identify equivalent expressions.
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Expression: \(2x−1−3.25x−9.75\)
- This simplifies correctly to \(-1.25x - 10.75\).
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Expression: \(2x−3.25x−1−9.75\)
- This simplifies correctly to \(-1.25x - 10.75\).
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Expression: \(−1.25x−1−9.75\)
- This simplifies to \(-1.25x - 10.75\).
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Expression: \(−1.25x−10.75\)
- This is already the simplified form derived.
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Expression: \(2x−1−3.25x+9.75\)
- This would result in \(2x - 3.25x - 1 + 9.75\), simplifying to \(-1.25x + 8.75\), which is not equivalent.
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Expression: \(1.25x + 10.75\)
- This is not equivalent, as it has incorrect signs and different constants.
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Expression: \(−1.25x−4\)
- This is not equivalent, as the constant term is incorrect.
Based on this analysis, 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 equivalent expressions are:
- \(2x−1−3.25x−9.75\)
- \(2x−3.25x−1−9.75\)
- \(−1.25x−1−9.75\)
- \(−1.25x−10.75\)
1 answer