To solve the absolute value inequality |x-2| ≤ 5 algebraically, we can break it down into two separate cases: Case 1: (x-2) ≥ 0 In this case, the absolute value of (x-2) is equal to (x-2). So we have the inequality (x-2) ≤ 5. To solve this inequality, we can add 2 to both sides to isolate x: (x-2) + 2 ≤ 5 + 2 x ≤ 7 So for x ≥ 2, the solution is x ≤ 7. Case 2: (x-2) < 0 In this case, the absolute value of (x-2) is equal to -(x-2), which means we need to change the inequality sign. So we have the inequality -(x-2) ≤ 5. To solve this inequality, we can multiply both sides by -1, which changes the direction of the inequality sign: -(x-2) * (-1) ≥ 5 * (-1) x-2 ≥ -5 Next, we can add 2 to both sides to isolate x: (x-2) + 2 ≥ -5 + 2 x ≥ -3 So for x < 2, the solution is x ≥ -3. Combining both cases, we have the final solution: x ≤ 7 for x ≥ 2, and x ≥ -3 for x < 2. However, none of the options provided in the answer choices match this solution. It appears that there may be a typo or error in the provided answer choices.