Problem: The symbol ∣a∣ means +a if a is greater than or equal to zero, and −a if a is less than or equal to zero; the symbol < means "less than"; the symbol > means "greater than."
The set of values x satisfying the inequality ∣3−x∣<4 consists of all x such that:
Answer Choices:
A. x2<49
B. x2>1
C. 1<x2<49
D. −1<x<7
E. −7<x<1
Solution:
Let AB be a straight line segment with its midpoint at 3, and its right end at B. Each of the two intervals from A to 3 and from 3 to B is less than 4. Hence B is to the left of 7 and A is to the right of −1.
or
∣3−x∣<4∴3−x<4−4<3−x∴−x<1∴−7<−x∴−1<x<7∴x>−1∴x<7