(0,7x-2,1)-(0,5-2x) =0,9(3x-1) +0,1

To solve the equation \((0.7x - 2.1) - (0.5 - 2x) = 0.9(3x - 1) + 0.1\), we will start by simplifying both sides.

1. Simplify the left-hand side: \[ (0.7x - 2.1) - (0.5 - 2x) = 0.7x - 2.1 - 0.5 + 2x \] Combine like terms: \[ = (0.7x + 2x) + (-2.1 - 0.5) = (2.7x) + (-2.6) = 2.7x - 2.6 \]

2. Simplify the right-hand side: \[ 0.9(3x - 1) + 0.1 = 0.9 \cdot 3x - 0.9 \cdot 1 + 0.1 \] Calculate: \[ = 2.7x - 0.9 + 0.1 \] Combine like terms: \[ = 2.7x - 0.8 \]

3. Set the simplified sides equal to each other: \[ 2.7x - 2.6 = 2.7x - 0.8 \]

4. Subtract \(2.7x\) from both sides: \[ -2.6 = -0.8 \]

5. Clearly \(-2.6\) does not equal \(-0.8\), meaning there are no values of \(x\) that satisfy this equation.

Therefore, the equation has no solution.