Algebra
# Absolute Value Inequalities

Solve for $x:$ $\frac{\lvert x^2 - 144 \rvert}{\lvert x^2 + 144 \rvert} < 1 .$

Solve for $x:$ $\lvert x^2 + 16 \rvert - \lvert x^2 - 16 \rvert > 2.$

Solve for $x:$ $\lvert x^2 + 288 \rvert < \lvert 288 - 2x^2 \rvert.$

Solve for $x:$ $\lvert x^2 \rvert < \lvert x^2 + 16x \rvert .$

Solve for $x:$ $\lvert x^2 + 36 \rvert < \lvert x^2 + 6x \rvert .$