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 \( 46 x-23=46 x+23 \)

To determine which of the given equations have infinitely many solutions, we need to analyze each equation step by step. An equation has infinitely many solutions if it simplifies to a true statement (like \(0 = 0\)) for all values of \(x\). Let's analyze each equation: ### A. \( -46x - 23 = 46x + 23 \) 1. Rearranging gives: \[ -46x - 46x = 23 + 23 \] \[ -92x = 46 \] \[ x = -\frac{46}{92} = -\frac{1}{2} \] This equation has a single solution, not infinitely many. ### B. \( -46x + 23 = 46x + 23 \) 1. Rearranging gives: \[ -46x - 46x = 23 - 23 \] \[ -92x = 0 \] \[ x = 0 \] This equation also has a single solution, not infinitely many. ### C. \( 46x + 23 = 46x + 23 \) 1. This equation is already in the form \(A = A\), which is always true for any value of \(x\). Thus, this equation has infinitely many solutions. ### D. \( 46x - 23 = 46x + 23 \) 1. Rearranging gives: \[ 46x - 46x = 23 + 23 \] \[ 0 = 46 \] This is a false statement, indicating that there are no solutions. ### Conclusion The only equation that has infinitely many solutions is: - **C** \( 46x + 23 = 46x + 23 \) So the answer is **C**.