0,5(8x+1=1,5-(2-4x)

Let's carefully interpret and solve the given equation step by step. **Given equation:** \[ 0,5(8x + 1) = 1,5 - (2 - 4x) \] **Step 1: Simplify both sides** On the left: \[ 0,5 \times 8x + 0,5 \times 1 = 4x + 0,5 \] On the right: \[ 1,5 - 2 + 4x = (1,5 - 2) + 4x = 0,5 + 4x \] **Updated equation:** \[ 4x + 0,5 = 0,5 + 4x \] **Step 2: Subtract \(4x\) from both sides:** \[ 4x + 0,5 - 4x = 0,5 + 4x - 4x \] \[ 0,5 = 0,5 \] This simplifies to a **true statement**, meaning **any real number \(x\)** satisfies this equation. --- ### **Answer:** **The equation has infinitely many solutions; all real numbers \(x\) satisfy it.**