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Absolute Value Inequalities

Absolute Value Inequalities - 2 or More quadratic Terms

Solve for \(x:\) \[\frac{\lvert x^2 - 144 \rvert}{\lvert x^2 + 144 \rvert} < 1 .\]

\[ {-12}<x<{12} \] \[x> {12} \] \[ x <{-12} \] \[ x < {0}, x > {0} \]

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by Brilliant Staff

Solve for \(x:\) \[\lvert x^2 + 16 \rvert - \lvert x^2 - 16 \rvert > 2. \]

\[ x < {-1} \] \[ x > {1} \] \[ {-1} < x < {1} \] \[ x < {-1}, x > {1} \]

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by Brilliant Staff

Solve for \(x:\) \[\lvert x^2 + 288 \rvert < \lvert 288 - 2x^2 \rvert. \]

\[ x > {-24} \] \[ x < {24}\] \[ {-24} < x < {24} \] \[ x < {-24}, x > {24} \]

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by Brilliant Staff

Solve for \(x:\) \[\lvert x^2 \rvert < \lvert x^2 + 16x \rvert .\]

\[ {-8}<x<{8} \] \[ {-8}<x<{0}, x>{0} \] \[x> {0}\] \[ {-8}<x<{0} \]

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by Brilliant Staff

Solve for \(x:\) \[\lvert x^2 + 36 \rvert < \lvert x^2 + 6x \rvert .\]

\[ {0}< x < {6} \] \[ x<{0} \] \[ x>{6} \] \[ x>{-6} \]

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by Brilliant Staff

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