A \( -75 x+57=-75 x+57 \) B \( 75 x+57=-75 x+57 \) C \( -57 x+57=-75 x+75 \) D \( 57 x+57=-75 x-75 \)

Let's analyze the equations provided in options A, B, C, and D. We will solve each equation step by step. ### Option A: \[ -75x + 57 = -75x + 57 \] This equation simplifies to \(0 = 0\), which is always true. Therefore, this equation is valid for all values of \(x\). ### Option B: \[ 75x + 57 = -75x + 57 \] To solve for \(x\), we can first subtract \(57\) from both sides: \[ 75x = -75x \] Now, add \(75x\) to both sides: \[ 75x + 75x = 0 \implies 150x = 0 \] Dividing both sides by \(150\): \[ x = 0 \] ### Option C: \[ -57x + 57 = -75x + 75 \] First, let's add \(75x\) to both sides: \[ -57x + 75x + 57 = 75 \] This simplifies to: \[ 18x + 57 = 75 \] Now, subtract \(57\) from both sides: \[ 18x = 18 \] Dividing both sides by \(18\): \[ x = 1 \] ### Option D: \[ 57x + 57 = -75x - 75 \] First, add \(75x\) to both sides: \[ 57x + 75x + 57 = -75 \] This simplifies to: \[ 132x + 57 = -75 \] Now, subtract \(57\) from both sides: \[ 132x = -132 \] Dividing both sides by \(132\): \[ x = -1 \] ### Summary of Solutions: - **Option A**: Valid for all \(x\) - **Option B**: \(x = 0\) - **Option C**: \(x = 1\) - **Option D**: \(x = -1\) If you need further analysis or specific information about any of these equations, please let me know!