To determine which expressions are equivalent to the algebraic expression \((3x−8)+(2x+5)−(4x−8)\), we first simplify the original expression step by step.
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Distribute the negative sign in front of \((4x−8)\): \[ (3x - 8) + (2x + 5) - 4x + 8 \]
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Combine like terms:
- For the \(x\) terms: \(3x + 2x - 4x = 1x\) or simply \(x\).
- For the constant terms: \(-8 + 5 + 8 = -8 + 5 + 8 = -8 + 13 = 5\).
So, the simplified expression is: \[ x + 5 \]
Now we can check each of the provided responses to see if they simplify to \(x + 5\).
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3x−8+2x+5−4x−8
- This simplifies to \(3x + 2x - 4x - 8 + 5 - 8 = x - 8 + 5 = x - 3\), which is not equivalent.
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3x−8+2x+5−4x+8
- This simplifies to \(3x + 2x - 4x - 8 + 5 + 8 = x + 5\), which is equivalent.
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3x+2x−4x−8+5+8
- This also simplifies to \(3x + 2x - 4x - 8 + 5 + 8 = x + 5\), which is equivalent.
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5x−4x−8+5+8
- This simplifies to \(x - 8 + 5 + 8 = x + 5\), which is equivalent.
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x−8+5+8
- This simplifies to \(x - 8 + 5 + 8 = x + 5\), which is equivalent.
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x−13+8
- This simplifies to \(x - 5\), which is not equivalent.
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x−3+8
- This simplifies to \(x + 5\), which is equivalent.
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x−21
- This is just \(x - 21\), which is not equivalent.
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x+5
- This is the expression itself, so it is equivalent.
Based on this evaluation, 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
So the final equivalent expressions selected are:
- \(3x−8+2x+5−4x+8\)
- \(3x+2x−4x−8+5+8\)
- \(5x−4x−8+5+8\)
- \(x−8+5+8\)
- \(x−3+8\)
- \(x+5\)
1 answer