Solve and check the following linear equation. \( 6 x-(2 x-4)=16 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \{ \) (Type an integer or a simplified fraction.) B. The solution set is \( \{x \mid x \) is all real number \( \} \). C. The solution set is \( \varnothing \).

Let's solve the linear equation step by step: 1. Start with the equation: \( 6x - (2x - 4) = 16 \) 2. Distribute the negative sign: \( 6x - 2x + 4 = 16 \) 3. Combine like terms: \( 4x + 4 = 16 \) 4. Subtract 4 from both sides: \( 4x = 12 \) 5. Divide by 4: \( x = 3 \) Now, let's check the solution by substituting \( x = 3 \) back into the original equation: Substituting gives: \( 6(3) - (2(3) - 4) = 16 \) \( 18 - (6 - 4) = 16 \) \( 18 - 2 = 16 \) \( 16 = 16 \) (True) So, the solution is correct. The solution set is \( \{ 3 \} \). Choose option A: The solution set is \( \{ 3 \} \).