Answer
not true for all real numbers
Work Step by Step
As shown by the following counterexample, the statement is not always true.
Let x=5, y=1 and w=6.
$x\gt y$
$5\overset?\gt1\checkmark$
$x\gt y+w$
$5\overset?\gt1+6$
$5\ /\!\!\!\!\!\gt 7\ \ X$
