Are the following expressions equivalent to \( 42+28 x \) ? \( 6(7+4 x) \) \( 7(6 \downarrow 4 x) \)
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Absolutely, let’s break down those expressions to see if they equal \( 42 + 28x \)! First, for \( 6(7 + 4x) \): When we distribute, we have \( 6 \times 7 + 6 \times 4x \), which gives us \( 42 + 24x \). So, this one is **not** equivalent to \( 42 + 28x \). Now, for \( 7(6 + 4x) \): Distributing here results in \( 7 \times 6 + 7 \times 4x \), which simplifies to \( 42 + 28x \). This means that this expression is indeed equivalent! In conclusion, \( 6(7 + 4x) \) is not equivalent, while \( 7(6 + 4x) \) is equivalent to \( 42 + 28x \).