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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Distribute the negative sign: \[ (3x - 8) + (2x + 5) - (4x - 8) = 3x - 8 + 2x + 5 - 4x + 8 \]
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Combine like terms: \[ (3x + 2x - 4x) + (-8 + 5 + 8) = (3 + 2 - 4)x + (-8 + 5 + 8) \] \[ = 1x + 5 = x + 5 \]
Now that we have simplified the original expression to \(x + 5\), let’s evaluate the provided responses:
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3x−8+2x+5−4x−8 This simplifies to \(x + 5\) (as shown above). Equivalent
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3x−8+2x+5−4x+8 This simplifies to \(x + 13\). Not Equivalent
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3x+2x−4x−8+5+8 This simplifies to \(x + 5\) (as shown above). Equivalent
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5x−4x−8+5+8 This simplifies to \(x + 5\) (as shown above). Equivalent
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x−8+5+8 This simplifies to \(x + 5\) (as shown above). Equivalent
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x−13+8 This simplifies to \(x - 5\). Not Equivalent
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x−3+8 This simplifies to \(x + 5\). Equivalent
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x−21 This simplifies to \(x - 21\). Not Equivalent
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x+5 This is directly equivalent to \(x + 5\). Equivalent
Based on this analysis, the equivalent expressions are:
- 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
Choose all expressions that are equivalent from the options provided.