1. **State the problem:** Solve the equation $5x - 3 [ x - (2x - 1)] = 3$ for $x$. 2. **Apply the distributive property inside the brackets:** First simplify the expression inside the square brackets. Inside the brackets: $x - (2x - 1) = x - 2x + 1 = -x + 1$ 3. **Rewrite the equation:** $$5x - 3(-x + 1) = 3$$ 4. **Distribute the $-3$ across $(-x + 1)$:** $$5x + 3x - 3 = 3$$ 5. **Combine like terms:** $$8x - 3 = 3$$ 6. **Isolate the variable term by adding 3 to both sides:** $$8x - 3 + 3 = 3 + 3$$ $$8x = 6$$ 7. **Solve for $x$ by dividing both sides by 8:** $$x = \frac{6}{8}$$ Show cancellation: $$x = \frac{\cancel{6}}{\cancel{8}} \times \frac{3}{4}$$ Simplify fraction: $$x = \frac{3}{4}$$ **Final answer:** $$x = \frac{3}{4}$$