Select the expressions that are equivalent to \( 2(7 n+9)+8 \) \[ \begin{array}{c}7 n+26 \\ 26 n+14 \\ 2(9+7 n)+8 \\ (7 n+9) 2+8\end{array} \]

First, let's simplify the expression \( 2(7n + 9) + 8 \). 1. Distribute the \( 2 \) across \( (7n + 9) \): \[ 2(7n) + 2(9) + 8 = 14n + 18 + 8 \] 2. Now, combine like terms: \[ 14n + 18 + 8 = 14n + 26 \] Now, let's check each expression for equivalency: 1. \( 7n + 26 \): Not equivalent, since it has a coefficient of \( 7 \) instead of \( 14 \). 2. \( 26n + 14 \): Not equivalent, since it changes both the coefficient of \( n \) and the constant term. 3. \( 2(9 + 7n) + 8 \): This is equivalent because if you distribute the \( 2 \), you get \( 2(7n) + 2(9) + 8 = 14n + 18 + 8 = 14n + 26 \). 4. \( (7n + 9)2 + 8 \): This is also equivalent because it can be written as: \[ 2(7n + 9) + 8 = 14n + 18 + 8 = 14n + 26 \] Thus, the equivalent expressions are: - \( 2(9 + 7n) + 8 \) - \( (7n + 9)2 + 8 \) Final answer: The expressions that are equivalent to \( 2(7n + 9) + 8 \) are \( 2(9 + 7n) + 8 \) and \( (7n + 9)2 + 8 \).