To determine which of the given expressions are equivalent to the original expression \((3x−8)+(2x+5)−(4x−8)\), we will simplify the original expression step by step.
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Distribute the negative sign in \(-(4x - 8)\): \[ (3x - 8) + (2x + 5) - 4x + 8 \]
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Combine like terms:
- \(3x + 2x - 4x\)
- Combine the constants: \(-8 + 5 + 8\)
Simplifying \(3x + 2x - 4x\): \[ 3x + 2x - 4x = 5x - 4x = x \]
Simplifying the constants: \[ -8 + 5 + 8 = -8 + 13 = 5 \]
So, the expression simplifies to: \[ x + 5 \]
Now, let's check which of the given options are equivalent to \(x + 5\):
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Option 1: \(3x−8+2x+5−4x−8\)
- This simplifies to \(x + 5\) (True)
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Option 2: \(3x−8+2x+5−4x+8\)
- This simplifies to \(x + 13\) (Not equivalent)
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Option 3: \(3x+2x−4x−8+5+8\)
- This simplifies to \(x + 5\) (True)
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Option 4: \(5x−4x−8+5+8\)
- This simplifies to \(x + 5\) (True)
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Option 5: \(x−8+5+8\)
- This simplifies to \(x + 5\) (True)
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Option 6: \(x−13+8\)
- This simplifies to \(x - 5\) (Not equivalent)
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Option 7: \(x−3+8\)
- This simplifies to \(x + 5\) (True)
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Option 8: \(x−21\)
- This is not equivalent (Not equivalent)
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Option 9: \(x+5\)
- This is equivalent (True)
So, the expressions that are equivalent to the original expression \( (3x−8)+(2x+5)−(4x−8) \) are:
- \(3x−8+2x+5−4x−8\)
- \(3x+2x−4x−8+5+8\)
- \(5x−4x−8+5+8\)
- \(x−8+5+8\)
- \(x−3+8\)
- \(x+5\)
Final List of Equivalent Expressions:
- \(3x−8+2x+5−4x−8\)
- \(3x+2x−4x−8+5+8\)
- \(5x−4x−8+5+8\)
- \(x−8+5+8\)
- \(x−3+8\)
- \(x+5\)
1 answer