1. **State the problem:** Determine if a triangle can be formed with side lengths 0.7, 1.4, and 2.1. 2. **Recall the Triangle Inequality Theorem:** For any triangle with sides $a$, $b$, and $c$, the sum of the lengths of any two sides must be greater than the length of the remaining side: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 3. **Apply the theorem to the given sides:** - Check $0.7 + 1.4 > 2.1$: $$0.7 + 1.4 = 2.1$$ - Check $0.7 + 2.1 > 1.4$: $$0.7 + 2.1 = 2.8 > 1.4$$ - Check $1.4 + 2.1 > 0.7$: $$1.4 + 2.1 = 3.5 > 0.7$$ 4. **Analyze the results:** The first inequality is $0.7 + 1.4 = 2.1$, which is not greater than 2.1 but equal to it. 5. **Conclusion:** Since the sum of two sides equals the third side and does not exceed it, the Triangle Inequality Theorem is not satisfied. Therefore, it is **not possible** to form a triangle with side lengths 0.7, 1.4, and 2.1.