Which of the following equations have infinitely many solutions? Choose all answers that apply: A \( -46 x-23=46 x+23 \) (B) \( -46 x+23=46 x+23 \) (C) \( 46 x+23=46 x+23 \) (D \( 46 x-23=46 x+23 \)

The equation in option (C) \( 46 x + 23 = 46 x + 23 \) is true for all values of \( x \), meaning it has infinitely many solutions since both sides are identical. Furthermore, option (B) \( -46 x + 23 = 46 x + 23 \) simplifies to \( -92 x = 0 \), leading to a unique solution \( x = 0 \). The other equations either lead to a contradiction or a unique solution, thus not having infinitely many solutions. To solve these types of equations efficiently, it's often helpful to simplify each equation step-by-step, isolating \( x \) as much as possible. Always check both sides of the equation afterward; if they become identical, congratulations—you have found infinite solutions! On the other hand, if you reach a contradiction like \( 0 = 1 \), you know those equations only have finite solutions or none at all.