Question

State true or false :
$x < \- y \Rightarrow - x > y$

Answer 1

In order to solve this question , we should know that Mathematics is not always about "equals", sometimes we only know that something is greater or less than. So the concept of Inequality is used here . An inequality compares the two values showing if one is less than , greater than , or simply not equal to another value , it could be less than or equal to and greater than or equal to – between two numbers or algebraic expressions . There are five types of inequality representing by relational symbol =>
$a \ne b$says that a is not equal to b .
$a < b$says that a is less than b .
$a > b$ says that a is greater than b .
$a \leqslant b$ says that a is less than or equal to b .
$a \geqslant b$ says that a is greater than or equal to b .

Complete step by step answer:
To solve the question given to us $x < \- y \Rightarrow - x > y$, here we can se equal to sign is not here that means we cannot simply multiply or divide . Rather there are differences in performing calculations with these inequalities .

There is a property that whenever we will perform multiplication with minus sign then the direction of the inequality changes by swapping the sides of the inequality which is shown as follows –
It is given that $x < \- y \Rightarrow - x > y$ thereafter ,
If $x < \- y$
Then on multiplying with negative sign (-ve) , the sign of inequality changes and it becomes
$- x > y$
Therefore , the given statement is true .

Note: Cross check that the answer is correct by verifying the direction of sign whenever there is multiplication of negative sign or -1 .
Use order of operations to evaluate expressions.
This can also be thought of a sign change, where the sides are swapped back to their original sides, but the signs change .
Besides that Solve inequalities using the same methods as solving equations, treating the <, >, as an = symbol .