This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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 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 0 Step 3: Solve the inequality for K. Subtract 2 from both sides of the inequality: K -2 Step 4: Express the solution in interval notation. The values of K that satisfy K -2 are all real numbers from -2 upwards, including -2. This is represented by the interval [-2, +[. Step 5: Compare with the given options. A. K ]-; 2] B. K [-2; +[ C. K ]-; a] D. K [-... (partially visible) The correct option is B. The final answer is B. K [-2; +[. Send me the next one 📸