1959 AMC 12 Question 25 - thichhoctoan.com

Question 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 $\lt$ means “less than”; the symbol $\gt$ means “greater than.” The set of values $x$ satisfying the inequality $|3-x|\lt4$ consists of all $x$ such that:

$x^2\lt49$
$x^2\gt1$
$1\lt x^2\lt49$
$-1\lt x\lt7$
$-7\lt x\lt1$