1. **State the problem:** We want to find the set $A = \{x \in \mathbb{R} \mid -1 \leq \frac{x-1}{2} < 3\}$. 2. **Understand the inequality:** The set $A$ contains all real numbers $x$ such that the expression $\frac{x-1}{2}$ is between $-1$ (inclusive) and $3$ (exclusive). 3. **Solve the compound inequality:** $$-1 \leq \frac{x-1}{2} < 3$$ Multiply all parts by 2 (positive number, so inequality signs remain the same): $$-2 \leq x - 1 < 6$$ 4. **Isolate $x$:** Add 1 to all parts: $$-2 + 1 \leq x < 6 + 1$$ $$-1 \leq x < 7$$ 5. **Interpret the solution:** The set $A$ is all real numbers $x$ such that $x$ is greater than or equal to $-1$ and less than $7$. **Final answer:** $$A = \{x \in \mathbb{R} \mid -1 \leq x < 7\}$$