1. **Problem Statement:** Solve the first equation from SET 1: $5(x - 1) = 35$. 2. **Formula and Rules:** To solve linear equations, distribute multiplication over addition/subtraction, combine like terms, and isolate the variable by performing inverse operations. 3. **Step-by-step Solution:** - Distribute 5: $$5x - 5 = 35$$ - Add 5 to both sides: $$5x - 5 + \cancel{(-5)} + 5 = 35 + 5$$ - Simplify: $$5x = 40$$ - Divide both sides by 5: $$\frac{5x}{\cancel{5}} = \frac{40}{\cancel{5}}$$ - Simplify: $$x = 8$$ 4. **Explanation:** We first remove parentheses by distributing 5. Then, we add 5 to both sides to isolate the term with $x$. Finally, dividing both sides by 5 gives the value of $x$. 5. **Final Answer:** $x = 8$