To determine which expressions are equivalent to the algebraic expression \((3x−8)+(2x+5)−(4x−8)\), we first simplify the original expression.
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Distribute and combine like terms: \[ (3x - 8) + (2x + 5) - (4x - 8) \] This can be written as: \[ 3x - 8 + 2x + 5 - 4x + 8 \]
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Combine the x terms: \[ (3x + 2x - 4x) + (-8 + 5 + 8) \] Simplifying the x terms: \[ 3x + 2x - 4x = x \] And simplifying the constant terms: \[ -8 + 5 + 8 = -8 + 5 + 8 = 5 \]
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Final simplified expression: The entire expression simplifies to: \[ x + 5 \]
Now we can evaluate the given options to see which are equivalent to \(x + 5\).
Responses:
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\(3x - 8 + 2x + 5 - 4x - 8\) (This is equivalent since we simplified it to \(x + 5\).)
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\(3x - 8 + 2x + 5 - 4x + 8\) (This simplifies to \(3x + 2x - 4x - 8 + 5 + 8 = x + 5\).)
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\(3x + 2x - 4x - 8 + 5 + 8\) (This also simplifies to \(x + 5\).)
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\(x - 13 + 8\) (This simplifies to \(x - 5\), which is not equivalent.)
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\(x - 21\) (This is clearly not equivalent.)
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\(x + 5\) (This is clearly equivalent as it is exactly \(x + 5\).)
Conclusion: The expressions that are equivalent to \( (3x−8)+(2x+5)−(4x−8) \) are:
- \(3x - 8 + 2x + 5 - 4x - 8\)
- \(3x - 8 + 2x + 5 - 4x + 8\)
- \(3x + 2x - 4x - 8 + 5 + 8\)
- \(x + 5\)