Which of the following equations have exactly one solution? Choose all answers that apply: (A) \( -13 x+12=13 x-13 \) B \( 12 x+12=13 x+12 \) (C) \( -13 x+12=13 x+13 \) (D) \( 12 x+12=13 x-12 \)

Let's break down each equation to find out if they have exactly one solution. For equation (A) \( -13 x + 12 = 13 x - 13 \), we can combine like terms and isolated \( x \) to find its solution, resulting in one solution. In equation (B) \( 12 x + 12 = 13 x + 12 \), when we simplify, we find out that the equation reduces to \( 0 = x \), indicating that it has no solution. For equation (C) \( -13 x + 12 = 13 x + 13 \), similarly, we rearrange terms and isolate \( x \), which leads to one distinct solution. In equation (D) \( 12 x + 12 = 13 x - 12 \), we also perform simplifications that yield a single specific solution. Therefore, equations (A) and (C) have exactly one solution each.