To find expressions equivalent to the algebraic expression \(3x - 80 + (2x + 5) - (4x - 8)\), we can first simplify the given expression step by step.
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Distribute the negative sign in front of \((4x - 8)\): \[ 3x - 80 + 2x + 5 - 4x + 8 \]
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Combine like terms:
- For the \(x\) terms: \(3x + 2x - 4x = (3 + 2 - 4)x = 1x = x\)
- For the constant terms: \(-80 + 5 + 8 = -80 + 13 = -67\)
So, the simplified expression is: \[ x - 67 \]
Equivalent Expressions
Now we can express this in different equivalent forms. Here are some equivalent expressions to \(x - 67\):
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Standard form: \[ x - 67 \]
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Adding and subtracting the same value: \[ x - 70 + 3 \] (Adding -70 and +3 gives -67)
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Factored form (expressing as a product if possible): \[ 1(x - 67) \]
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Rearranged form: \[ -67 + x \]
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Expressing in terms of a different variable: \[ y = x - 67 \quad \text{where } y \text{ is another variable} \]
All these forms maintain the same value as the original expression, thus are equivalent.