Select the expressions that are equivalent to \( 5(-7 z+5) \). \[ \begin{array}{c}5(-8 z+z+5) \\ -35 z+25 \\ (-7 z+5) 5 \\ -7 z+25\end{array} \]

To determine which expressions are equivalent to \( 5(-7z + 5) \), we first simplify it: \[ 5(-7z + 5) = 5 \cdot -7z + 5 \cdot 5 = -35z + 25 \] Now, let's check each expression provided: 1. **\( 5(-8z + z + 5) \)** Simplifying inside the parentheses gives us: \(-8z + z = -7z\) So, we have: \[ 5(-7z + 5) = -35z + 25 \] (which is equivalent to our original) 2. **\(-35z + 25\)** This is exactly what we derived initially: \[-35z + 25\] (which is equivalent) 3. **\((-7z + 5) 5\)** Rewriting this using the commutative property gives us: \[ 5(-7z + 5) = -35z + 25 \] (which is equivalent) 4. **\(-7z + 25\)** This does not match our initial expression after simplification; it should be multiplied by 5 to be equivalent. \[-7z + 25\] (not equivalent) In conclusion, the equivalent expressions are: - \( 5(-8z + z + 5) \) - \( -35z + 25 \) - \((-7z + 5) 5\) The expression \(-7z + 25\) is not equivalent to \( 5(-7z + 5) \).