Solve and check the following linear equation. \[ \begin{array}{l}5 x-(3 x-5)=17 \\ \text { A. The solution set is }\{ \\ \text { (Type an integer or a simplified fraction.) } \\ \text { B. The solution set is }\{x \mid x \text { is all real number }\} \text {. } \\ \text { C. The solution set is } \varnothing \text {. }\end{array} \text {. } \]

Let's solve the equation step by step: The equation is: \[ 5x - (3x - 5) = 17 \] First, simplify the left side: \[ 5x - 3x + 5 = 17 \] \[ 2x + 5 = 17 \] Now, isolate \(x\) by subtracting 5 from both sides: \[ 2x = 17 - 5 \] \[ 2x = 12 \] Next, divide both sides by 2: \[ x = 6 \] So, the solution set is \(\{6\}\). Now, let's check the solution by substituting \(x = 6\) back into the original equation: \[ 5(6) - (3(6) - 5) = 17 \] \[ 30 - (18 - 5) = 17 \] \[ 30 - 13 = 17 \] \[ 17 = 17 \] Since this is true, the solution is verified. The answer is: **A. The solution set is \{6\}.**