Which statement completes the syllogism? a. if |x| < a for some positive number a, then x < a. b. c. if |x| < a for some positive number a, then x > –a. question 3 options: a) if |x| < a for some positive number a, then x < a. b) if |x| < a for some positive number a, then x > –a. c) if x < a then x > –a. d) if x > –a then x < a.

Option C is correct i.e., if x < a then x > -a.

Step-by-step explanation:

if |x| < a for some positive number a,

then by solving the inequality,

we get, -a < x < a   (1)

i.e., x lies between -a and a.

from equation (1),if x < a then x > -a (which should be statement b)

So, we can say that If |x| < a for some positive number a, then x < a and x > –a (which is statement a and c).

so, the correct option is C i.e., if x < a then x > -a.