Triangle Inequality: Explained with Examples

[kingyof2thejring]

|(x-1)^2-5x+4|=|(x-1)^2 - 3(x-1)| <= |x-1|^2+3|x-1|
how does that work? i thought triangle inequaility was |x+y| <= |x|+|y|
please explain thanks in advance

 

[quasar987]

Well the first equality is false. - 3(x-1) $\neq$-5x+4. But the inequality is correct. The triangle inequaity says that

|x±y|$\leq$|x|+|y|