Could someone please check my proof

4 Q 3 1. Prove ( 1x1-141 / 5/ x-yl. Reverse Triangle Jrepudity 1 *1- 14/ 5 / x-41 iff ( x- 4 + 4 1 - 14 1 = 1 x - yl iff [ x-y+y / = ( x-yl + 14) by Theorem 1. 9. 8 for The Triangle Inequality 1* 1- 17 / 2 -1 x-41 iff - 1 x / + ly / = / x - yl iff 14 / = 1 x - 4 / + 1 * 1 iff 141 = 1 7 - x / + 1 * 1 iff | y- x + x/ = / x-x1 + /x1 by Theorem 11. 9.d for the Triangle Inequality Since / x 1 - 171 = ( x - 4/ and ( x 1 - 14 / 2 - 1 x-4/ Then 1x 1 - 141 5 / x - y) by Theorem 11. 9. 6