Select the expressions that are equivalent to \( (7 g+3)+(g-5) \). \[ \begin{array}{c}-2 g+8 \\ -2+g+7 g \\ (3 g+7)+(g-5) \\ (3 g+7)+(-5 g+1)\end{array} \]

First, let's simplify the expression \( (7g + 3) + (g - 5) \). 1. Combine like terms: \[ 7g + g + 3 - 5 = 8g - 2. \] So \( (7g + 3) + (g - 5) \) simplifies to \( 8g - 2 \). Now let's check each of the expressions to see which are equivalent: 1. **Expression 1:** \(-2g + 8\) Not equivalent, since \(8g - 2 \neq -2g + 8\). 2. **Expression 2:** \(-2 + g + 7g\) Simplifies to \(-2 + 8g\), which is \(8g - 2\). This is equivalent. 3. **Expression 3:** \((3g + 7) + (g - 5)\) Simplifies to \(3g + g + 7 - 5 = 4g + 2\). Not equivalent. 4. **Expression 4:** \((3g + 7) + (-5g + 1)\) Simplifies to \(3g - 5g + 7 + 1 = -2g + 8\). Not equivalent. Thus, the expressions equivalent to \( (7g+3)+(g-5) \) is: \[ \boxed{(g + 7g - 2)}. \]