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.