Question

How do you know by inspection that the solution set of the inequality x+3>x+2 is the entire set of real numbers?

Decimals
How do you know by inspection that the solution set of the inequality $$x+3>x+2$$ is the entire set of real numbers?

2021-05-30
Step 1
It is given that,
$$x+3>x+2$$
Here on both side of the inequality positive quantities added so it doesn't matter whatever the value of the 'x', you will always found that the expression is always correct for each real value. Real value can be any negative, positive or in decimals.
Step 2
It is well known that the set is real numbers is defined as,
$$[-\infty,\ \infty]$$