To determine which expressions are equivalent to the algebraic expression \( 5(3x + 9) \), let’s simplify it:
- Distribute the 5: \[ 5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45 \]
Now we have simplified \( 5(3x + 9) \) to \( 15x + 45 \).
Next, we will compare this result with each expression provided:
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\( 8x + 14 \) - Not equivalent, since it is neither in the form of \( 15x + 45 \).
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\( 5 \cdot 3x + 5 \cdot 9 \) - This is equivalent since it simplifies to \( 15x + 45 \).
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\( 5 \cdot 3x + 9 \) - Not equivalent, since it simplifies to \( 15x + 9 \), which is not the same.
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\( 15x + 9 \) - Not equivalent, it does not match \( 15x + 45 \).
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\( 15x + 45 \) - Equivalent, this matches exactly with our simplified expression.
Based on this analysis, the equivalent expressions to \( 5(3x + 9) \) are:
- \( 5 \cdot 3x + 5 \cdot 9 \)
- \( 15x + 45 \)
1 answer