Could someone please check my work

1. Prove / 1* 1 - 141 5 / x- 41 . 1 X1- 14/ 5/ x-41 iff / x - 4 + 4 1 - 14 1 = / * - 4 ) iff [ x-y+y / = / x- y/ + 141 by Theorem 11. 9. 8 for The Triangle Inequality 1* 1-14/2 - 1x-41 iff - 1 x / + 14/ =1 x- 71 iff |4 / = )x- 4 / + / * 1 ifF 141 = 14 - * 1 + 1 * 1 iff | y - x + x ) = / Y- x) + / x) by Theorem 11. 9.d for The Triangle Inequality Since / * 1- 171 = ( x- 41 and | * 1 - 14/ 2 - 1x-4/ Then |1x 1 - 141 5 / x - y / by Theorem 11. 9. 6