For each equation, choose the statement that describes its solution. If applicable, give the solution. \begin{tabular}{l} (a) \( -2(w+6)-6 w=4(w+3) \) \\ No solution \\ All real numbers are solutions \\ (b) \( 4(3+u)-u=6+3(u+2) \) \\ No solution \\ All real numbers are solutions \\ \hline\end{tabular}

Let's analyze each equation to determine their solutions. ### (a) \( -2(w + 6) - 6w = 4(w + 3) \) **Step-by-Step Solution:** 1. **Expand both sides:** \[ -2w - 12 - 6w = 4w + 12 \] 2. **Combine like terms:** \[ -8w - 12 = 4w + 12 \] 3. **Move all terms involving \( w \) to one side and constants to the other:** \[ -8w - 4w = 12 + 12 \] \[ -12w = 24 \] 4. **Solve for \( w \):** \[ w = \frac{24}{-12} = -2 \] **Conclusion:** There is a unique solution, \( w = -2 \). ### (b) \( 4(3 + u) - u = 6 + 3(u + 2) \) **Step-by-Step Solution:** 1. **Expand both sides:** \[ 12 + 4u - u = 6 + 3u + 6 \] 2. **Combine like terms:** \[ 12 + 3u = 12 + 3u \] 3. **Subtract \( 12 + 3u \) from both sides:** \[ 0 = 0 \] **Conclusion:** This is an identity, meaning **all real numbers** are solutions. ### Summary of Solutions: - **(a)** The solution is \( w = -2 \). - **(b)** **All real numbers** are solutions.