The inequalities for some absolute value functions are not correct

The inequality image should be true for all real numbers, but when graphed it shows it is true for x > 0 or x = 0.

Thanks for the report. Our implicit equation plotter has some limitations: it only plots curves (not areas), and it only plots boundaries between positive and negative regions (after subtracting the RHS from the LHS). Therefore, it can’t find solutions that “kiss” 0 without crossing it.