Can someone show me my mistake. I keep getting |a - b| <= |a| - |b| and it should be the opposite.

-|a| <= a <= |a|

-|b| <= b <= |b| //subtract them

-|a| + b <= a - b <= |a| - |b|

-(|a| - |b|) <= a - b <= |a| - |b| //therefore

|a-b| <= |a| - |b|

Thanks

(sorry I didn't use latex. I keep getting the math error sign)