# Write the set of values of x satisfying the inequation

Question:

Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.

Solution:

We have,

$\left(x^{2}-2 x+1\right)(x-4)<0$

$\Rightarrow(x-1)^{2}(x-4)<0$

Equating each one to zero, we obtain $\mathrm{x}=1$ and $\mathrm{x}=4$.

Therefore, 1 and 4 are critical points.

Drawing the number lines, we get:

Therefore, the solution set of the given inequality is $x \in(-\infty, 1) \cup(1,4)$