To determine which expressions are equivalent to \( 5(x + 3) - 4 \), let's simplify that expression step by step.
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Distribute \( 5 \) in the expression: \[ 5(x + 3) = 5x + 15 \]
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Subtract \( 4 \) from the result: \[ 5x + 15 - 4 = 5x + 11 \]
Now we have simplified \( 5(x + 3) - 4 \) to \( 5x + 11 \).
Next, let's compare with the given options:
- \( 5x - 1 \)
- \( 5x + 15 - 4 \) (This simplifies to \( 5x + 11 \))
- \( 5x - 5 \)
- \( 5x + 11 \)
- \( 5x + 3 - 4 \) (This simplifies to \( 5x - 1 \))
The two expressions equivalent to \( 5(x + 3) - 4 \) are:
- \( 5x + 15 - 4 \) (which simplifies to \( 5x + 11 \))
- \( 5x + 11 \)
So, the two correct responses are:
- \( 5x + 15 - 4 \)
- \( 5x + 11 \)