To determine which expressions are equivalent to the original expression \((3x−8)+(2x+5)−(4x−8)\), we can simplify the original expression step by step.
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Start with the original expression: \[ (3x - 8) + (2x + 5) - (4x - 8) \]
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Distribute the negative sign to the third term: \[ (3x - 8) + (2x + 5) - 4x + 8 \]
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Rearrange the expression: \[ 3x + 2x - 4x - 8 + 5 + 8 \]
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Combine like terms:
- Combine the \(x\) terms: \(3x + 2x - 4x = x\)
- Combine the constant terms: \(-8 + 5 + 8 = 5\)
Thus, the simplified expression is: \[ x + 5 \]
Now, let's evaluate the provided responses to see which ones simplify to \(x + 5\):
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Response: \(3x−8+2x+5−4x−8\)
- Equivalent to the original, simplifies to \(x + 5\)
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Response: \(3x−8+2x+5−4x+8\)
- This simplifies to \(x + 1\), not equivalent.
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Response: \(3x + 2x - 4x - 8 + 5 + 8\)
- Equivalent to the original, simplifies to \(x + 5\)
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Response: \(5x − 4x − 8 + 5 + 8\)
- Simplifies to \(x + 5\)
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Response: \(x − 8 + 5 + 8\)
- Simplifies to \(x + 5\)
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Response: \(x − 13 + 8\)
- Simplifies to \(x - 5\), not equivalent.
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Response: \(x − 3 + 8\)
- Simplifies to \(x + 5\)
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Response: \(x − 21\)
- Simplifies to \(x - 21\), not equivalent.
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Response: \(x + 5\)
- This is already \(x + 5\), equivalent.
Summary of Equivalent Expressions:
The following responses are equivalent to the original expression \(x + 5\):
- \(3x−8+2x+5−4x−8\)
- \(3x + 2x - 4x - 8 + 5 + 8\)
- \(5x − 4x − 8 + 5 + 8\)
- \(x − 8 + 5 + 8\)
- \(x − 3 + 8\)
- \(x + 5\)
So the correct answers are the first, third, fourth, fifth, seventh, and the last option.
1 answer