Question

State true or false of the following :
If a and b are whole numbers and a < b , then $a + 1 < b + 1$

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 $a + 1 < b + 1$, here we can set equal sign is not here that means we cannot simply multiply or divide . Rather there are differences in performing calculations with these inequalities .

Here we will perform addition and so that Solve inequalities using the same methods as solving equations for addition and subtraction remain the same , treating the <, >, as an = symbol . But here we are to add + 1 to both the sides of the inequality . Besides that Solve inequalities using the same methods as solving equations, treating the <, >, as an = symbol .

According to our question , given is a and b are whole numbers , $a < b$.

Then on adding 1 both the sides of the inequality we get , the sign of inequality remains same and it becomes as follows -
$a + 1 < b + 1$
Therefore , the given statement is true .

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