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# Absolute Value Inequalities

Is a company's profit greater in magnitude than its loss? When is the error in the length of a candy bar acceptable to the factory?

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

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