I have the following inequality: $$|4 - k^2| > |10 + 13k|$$ So how to solve this ?
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Start by sketching the graphs $y=|4-x^2|$ and $y=|10+13x|$. To do this, sketch $y=4-x^2$ and $y=10+13x$ and reflect anything below the $x$-axis back up above the $x$-axis.
Next, solve the two equations $4-x^2 = \pm(10+13x)$.
Use your sketch to help you find the regions where $|4-x^2| > |10+13x|$.