Question

1. solve the inequality: |x - 6| - 6 < -4

a. 3 < x ≤ 9
b. 4 < x < 8
c. x ≥ 10 or x ≤ -2
d. -3 < x < 1

Explanation:

Step1: Isolate the absolute value

Start with the inequality \(|x - 6| - 6 < -4\). Add 6 to both sides to isolate the absolute value term:
\(|x - 6| < -4 + 6\)
\(|x - 6| < 2\)

Step2: Solve the absolute value inequality

The absolute value inequality \(|a| < b\) (where \(b>0\)) is equivalent to \(-b < a < b\). So for \(|x - 6| < 2\), we have:
\(-2 < x - 6 < 2\)

Step3: Solve for x

Add 6 to all parts of the compound inequality:
\(-2 + 6 < x < 2 + 6\)
\(4 < x < 8\)

Answer:

B. \(4 < x < 8\)