1. **State the problem:** List all elements in the set $A = \{x \in \mathbb{Z}^+ : (x^2 - 4) < 10\}$. 2. **Understand the set definition:** $A$ contains all positive integers $x$ such that $x^2 - 4 < 10$. 3. **Write the inequality:** $$x^2 - 4 < 10$$ 4. **Solve the inequality:** Add 4 to both sides: $$x^2 < 14$$ 5. **Find all positive integers $x$ satisfying $x^2 < 14$:** Since $x$ is positive integer, check squares: - $1^2 = 1 < 14$ - $2^2 = 4 < 14$ - $3^2 = 9 < 14$ - $4^2 = 16 \not< 14$ So, $x = 1, 2, 3$ satisfy the inequality. 6. **Final answer:** $$A = \{1, 2, 3\}$$