Match the equations to their solution. Select all the equations that have the same solution as the equation below. \( 2 a=-4 \)

To determine which equations have the same solution as \( 2a = -4 \), let's first solve for \( a \): \[ 2a = -4 \] **Step 1: Solve for \( a \)** Divide both sides of the equation by 2: \[ a = \frac{-4}{2} = -2 \] **Solution:** \( a = -2 \) --- **Identifying Equivalent Equations** Any equation that simplifies to \( 2a = -4 \) when solved for \( a \) will have the same solution \( a = -2 \). Here are some examples of such equations: 1. **Equivalent Forms:** - \( -4 = 2a \) - \( a + a = -4 \) - \( 4a = -8 \) *(After dividing both sides by 2, it becomes \( 2a = -4 \))* - \( -2a = 4 \) *(After dividing both sides by -2, it becomes \( a = -2 \))* 2. **Using Operations:** - \( 2(a + 1) = -2 \) *(Expanding: \( 2a + 2 = -2 \), then \( 2a = -4 \))* - \( \frac{a}{-0.5} = -4 \) *(Multiplying both sides by -0.5: \( a = -2 \))* - \( 5a + 3a = -4 \) *(Combining like terms: \( 8a = -4 \), then \( a = -0.5 \))* - *Note: This last example does **not** have the same solution. Make sure to verify each equation's solution.* --- **Conclusion** Without specific equations to choose from, the general approach is to: 1. **Solve the given equation** to find the value of \( a \). 2. **Compare other equations** by solving them to see if they yield the same value for \( a \). If you provide a list of equations, I can help identify which ones have the solution \( a = -2 \).