Problem: Find the set of x-values satisfying the inequality ∣∣∣∣∣35−x∣∣∣∣∣<2. [The symbol ∣a∣ means +a if a is positive, −a if a is negative, 0 if a is zero. The notation 1<a<2 means that a can have any value between 1 and 2 , excluding 1 and 2.]
Answer Choices:
A. 1<x<11
B. −1<x<11
C. x<11
D. x>11
E. ∣x∣<6
Solution:
The numerical value of ∣5−x∣ must be less than 6 for the inequality to hold. Therefore, x must be greater than −1 , and less than 11 .
or
∣∣∣∣∣35−x∣∣∣∣∣<2,−2<35−x<2,−6<5−x<6
∴−6<5−x; x<11
and 5−x<6; x>−1
∴−1<x<11