Answer
Not true for all real numbers
Work Step by Step
The following counterexample shows that the inequality is not true for all real numbers.
Let x=2 and let y=-3.
$x+y\gt x-y\longrightarrow$ substitute the given values
$2+(-3)\overset?\gt 2-(-3)\longrightarrow$ simplify
$-1\ /\!\!\!\!\!\gt5$
When y is negative, the inequality is not true.
