1959 AHSME Problem 25

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: \textbf{(A)}\ x^2<49 \qquad\textbf{(B)}\ x^2>1 \qquad\textbf{(C)}\ 1<x^2<49\qquad\textbf{(D)}\ -1<x<7\qquad\textbf{(E)}\ -7<x<1

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.