Question

solve the inequality. |a - 6| < 8
no real solutions
all real numbers
-2 < a < 14
a < 14
a < -2 or a > 14

Explanation:

Step1: Apply absolute - value rule

If \(|x|0\)), then \(-k < x < k\). Here \(x=a - 6\) and \(k = 8\), so \(-8 < a-6 < 8\).

Step2: Add 6 to all parts

Adding 6 to each part of the compound - inequality \(-8 < a - 6<8\) gives \(-8+6 < a-6 + 6<8 + 6\).
\(-2 < a<14\)

Answer:

C. \(-2 < a < 14\)