2,6z - 0,2(3z-9)=-0,5(2z+6)

To solve the equation \( 2.6z - 0.2(3z - 9) = -0.5(2z + 6) \), we can start by distributing the terms in the equation. 1. Distribute \( -0.2 \) and \( -0.5 \): \[ 2.6z - 0.2 \cdot 3z + 0.2 \cdot 9 = -0.5 \cdot 2z - 0.5 \cdot 6 \] This simplifies to: \[ 2.6z - 0.6z + 1.8 = -1z - 3 \] 2. Combine like terms on the left side: \[ (2.6z - 0.6z) + 1.8 = -1z - 3 \] This gives: \[ 2z + 1.8 = -1z - 3 \] 3. Now, add \( 1z \) to both sides to combine all \( z \) terms on the left: \[ 2z + 1z + 1.8 = -3 \] This simplifies to: \[ 3z + 1.8 = -3 \] 4. Next, subtract \( 1.8 \) from both sides: \[ 3z = -3 - 1.8 \] Which simplifies to: \[ 3z = -4.8 \] 5. Finally, divide both sides by 3 to solve for \( z \): \[ z = \frac{-4.8}{3} = -1.6 \] Thus, the solution is: \[ \boxed{-1.6} \]