Answer
$(-1/2, 1/2)$
Work Step by Step
$1/4*x^2 < 1/16$
$4*1/4*x^2 <4* 1/16$
$x^2 < 1/4$
$\sqrt {x^2} < \sqrt {1/4}$
$x < ±1/2$
$x < 1/2$
$x < -1/2$
Three regions to test: $(-∞, -1/2)$, $(-1/2, 1/2)$, $(1/2, ∞)$
Let $x=-1$, $x=0$, $x=1$
$x=-1$
$1/4*x^2 < 1/16$
$1/4*(-1)^2 < 1/16$
$1/4 * 1 < 1/16$
$1/4 < 1/16$ (false)
$x=0$
$1/4*x^2 < 1/16$
$1/4*0^2 < 1/16$
$1/4*0 < 1/16$
$0 < 1/16$ (true)
$x=1$
$1/4*x^2 < 1/16$
$1/4*(1)^2 < 1/16$
$1/4 * 1 < 1/16$
$1/4 < 1/16$ (false)
