solve the inequality. |a - 6| < 8\nno real solutions\nall real numbers\n-2 < a < 14\na < 14\na < -2 or a > 14

Explanation:

Step1: Apply absolute - value rule

If (|x|\lt y) ((y>0)), then (-y\lt x\lt y). Here (x = a - 6) and (y = 8), so (-8\lt a - 6\lt8).

Step2: Add 6 to all parts

Adding 6 to each part of the compound - inequality (-8\lt a - 6\lt8) gives (-8+6\lt a-6 + 6\lt8 + 6). (-2\lt a\lt14)

Answer:

C. (-2\lt a\lt14)