Absolute Value Inequalities

Solve for $x:$ $\lvert x^2-1 \rvert > 2.$

Solve for $x:$ $\frac{1}{\lvert x^2-15 \rvert} > \frac{1}{15}.$

-\sqrt{15}<x<\sqrt{15}

-\sqrt{30}<x<\sqrt{30}

-\sqrt{30}<x<{0}, {0}<x<\sqrt{30}

-\sqrt{30}<x<-\sqrt{15}, -\sqrt{15} < x < {0}, {0} < x < \sqrt{15}, \sqrt{15} < x < \sqrt{30}

Solve for $x:$ $\lvert x^2-16x \rvert < 32x .$

Solve for $x:$ $\lvert x^2-13 \rvert < 13.$

-\sqrt{{26}}<x<{0}, {0} < x < \sqrt{{26}}

-2\sqrt{{26}}<x< 2\sqrt{{26}}

-\sqrt{{26}}<x< \sqrt{{26}}

-2\sqrt{{26}}<x<{0}, {0} < x < 2\sqrt{{26}}

Solve for $x:$ $\lvert x^2-32x \rvert < x^2 .$

Absolute Value Inequalities - 1 Quadratic Term