Fresh day armindarafaelmatsimbe, let's solve. Step 1: Understand the condition for an absolute value equation to have a solution. For an equation of the form $|X| = Y$ to have a solution, the right-hand side $Y$ must be non-negative, i.e., $Y \ge 0$. This is because the absolute value of any real number is always greater than or equal to zero. Step 2: Apply the condition to the given equation. The given equation is $|x-a| = 2+K$. Here, $X = x-a$ and $Y = 2+K$. For this equation to have a solution, we must have: $$2+K \ge 0$$ Step 3: Solve the inequality for $K$. Subtract 2 from both sides of the inequality: $$K \ge -2$$ Step 4: Express the solution in interval notation. The values of $K$ that satisfy $K \ge -2$ are all real numbers from -2 upwards, including -2. This is represented by the interval $[-2, +\infty[$. Step 5: Compare with the given options. A. $K \in ]-\infty; 2]$ B. $K \in [-2; +\infty[$ C. $K \in ]-\infty; a]$ D. $K \in [-...$ (partially visible) The correct option is B. The final answer is $\boxed{\text{B. } K \in [-2; +\infty[}$. Send me the next one 📸