If 5−x>1+5x and 5−3x≥2−4x, then x can take which of the following values?

Let's solve both linear inequalities independently.
First Inequality:

5−x>1+5x
Move x terms to one side and constants to the other:

5−1>5x+x
4>6x
x<
6
4
​
⟹x<
3
2
​
≈0.67
Second Inequality:

5−3x≥2−4x
Move x terms to one side and constants to the other:

−3x+4x≥2−5
x≥−3
Combining both conditions:

−3≤x<
3
2
​

Let's check the given options to see which value falls in the interval [−3,0.67):

A) 1 (Incorrect, 1>0.67)

B) 2 (Incorrect, 2>0.67)

C) −2 (Correct, −3≤−2<0.67)

D) −4 (Incorrect, −4<−3)

Therefore, x can take the value −2.