Solve the Inequality $\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$

question 124

Multiple Choice

Solve the inequality. Graph the solution set and write the solution set in interval notation.
- $\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$

• A) \(( - \infty , - 3 ] \cup ( - 2 , - 1 ) \cup [ 1 , \infty )\)
• B) \(( - \infty , 1 ) \cup ( 3 , \infty )\)
• C) \(( - \infty , 1 ] \cup [ 3 , \infty )\)
• D) \(( - \infty , - 3 ) \cup ( - 1 , \infty )\)

---

Definitions:

Hindbrain

The posterior part of the brain comprising structures including the cerebellum and brainstem, responsible for regulating basic functions such as heartbeat and respiration.

Brainstem

The posterior part of the brain, adjoining and structurally continuous with the spinal cord, responsible for vital life functions such as breathing, heart rate, and blood pressure.

Midbrain

An area of the brainstem involved in vision, hearing, motor control, sleep/wake, arousal (alertness), and temperature regulation.

Caffeine

A stimulant of the central nervous system found in coffee, tea, chocolate, and various medications, known for its ability to reduce fatigue and improve concentration.