Question

Solve for x: (|x|-1) / (|x|-2) > 5

Answer 1

Answer:

x−1∣−5∣≥2

((x−1)−5)∈(−∞,−2)∪(2,0)

−∞<∣x−1∣−5≤−2 2≤∣x−1∣−5<∞

−∞<∣x−1∣≤3 7≤∣x−1∣<∞

⇒∣x−1∣≤3 ⇒∣x−1∣≥7

−3≤(x−1)≤3 ⇒(x−1)∈(−∞,−7)∪[7,∞]

⇒

−2≤x≤4

x∈(−∞.−6)∪[8,∞]

∴x∈[−∞,−6]∪[−2,4]∪[8,∞]