To find the two expressions that are equivalent to \( 4(x+3)-10+6x \), let's first simplify the given expression step by step.
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Distribute \( 4 \) in the expression: \[ 4(x+3) = 4x + 12 \]
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Substitute this back into the expression: \[ 4x + 12 - 10 + 6x \]
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Combine like terms: \[ (4x + 6x) + (12 - 10) = 10x + 2 \]
Now, we see that the original expression simplifies to \( 10x + 2 \).
Next, let's analyze the response options to see which ones are equivalent to \( 10x + 2 \).
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\( 4x + 12 - 10 + 6x \)
- This simplifies to \( 10x + 2 \), which is equivalent.
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\( -2x - 7 \)
- This is not equivalent.
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\( 2(5x + 1) \)
- This simplifies to \( 10x + 2 \), which is equivalent.
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\( 10x - 7 \)
- This is not equivalent.
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\( 2(8x + 1) \)
- This simplifies to \( 16x + 2 \), which is not equivalent.
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\( 4x + 3 - 10 + 6x \)
- This simplifies to \( 10x - 7 \), which is not equivalent.
Thus, the TWO expressions that are equivalent to the original expression are:
- \( 4x + 12 - 10 + 6x \)
- \( 2(5x + 1) \)