1. The problem asks for a compound inequality describing the possible lengths of the third side $x$ of a triangle with two sides 0.8 and 1.4. 2. According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. 3. This gives us three inequalities: - $x + 0.8 > 1.4$ - $x + 1.4 > 0.8$ - $0.8 + 1.4 > x$ 4. Simplify each: - $x > 1.4 - 0.8$ - $x > 0.8 - 1.4$ - $2.2 > x$ 5. Calculate the values: - $x > 0.6$ - $x > -0.6$ (which is always true since side lengths are positive) - $x < 2.2$ 6. Combining the valid inequalities, the compound inequality describing $x$ is: $$0.6 < x < 2.2$$ This means the third side must be longer than 0.6 and shorter than 2.2 to form a valid triangle.