# Step-by-Step Solution ## Problem Statement Given the equation: \[ x + 2(x-1) + 3(x-2) = \] Solve for \(x\). --- ## Step 1: Expand the Equation Expand each term: - \(x\) stays as is. - \(2(x-1) = 2x - 2\) - \(3(x-2) = 3x - 6\) So the equation becomes: \[ x + 2x - 2 + 3x - 6 = \] --- ## Step 2: Combine Like Terms Add the \(x\) terms: \(x + 2x + 3x = 6x\) Add the constants: \(-2 - 6 = -8\) So, the equation is: \[ 6x - 8 = \] --- ## Step 3: Solve for \(x\) Add 8 to both sides: \(6x = 8\) Divide both sides by 6: \(x = \frac{8}{6}\) Simplify the fraction: \(x = \frac{4}{3}\) --- ## Final Answer The solution is \[ \boxed{x = \frac{4}{3}} \]