inequality

Solve the inequality: x²(3 – x)(x – 2)²(x + 4)³ > 0

 

Answer:

The LHS can be rewritten as {x(x – 2)(x + 4)}²(3 – x)(x + 4) > 0

Now since, {x(x – 2)(x + 4)}² > 0

Therefore, the inequality boils down to proving (3 – x)(x + 4) > 0

This condition can be satisfied under 2 conditions, namely;

Condition 1

(3 – x) > 0

(x + 4) > 0

ð  X < 3

ð  X > - 4

ð  -4 < x < 3

Condition 2

(3 – x) < 0

(x + 4) < 0

ð  X > 3

ð  X < - 4

ð  These values  do not satisfy the condition

So, the answer is -4 < x < 3