Question

How do you solve and write the following in interval notation: $x < 5$ and $x < 3$?

Answer 1

From the question we have been asked to solve and write the following in interval notation: $x < 5$ and $x < 3$.We can solve the given question by exploring the given conditions. We can write it in the interval notation by using some mathematical symbols.

Complete step-by-step solution:
From the question, we have been given that $x < 5$ and $x < 3$.
First of all, let us take the first condition $x < 5$
The given condition says that, if we put any integer or number in the variable $x$, that number should be less than $5$.
Now, let us take the second condition given in the question $x < 3$
The given condition says that, if we put any integer or number in the variable $x$, that number should be less than $3$.
Now, from both the conditions, we got one common point, that is,
The variable $x$ should be less than $3$ to satisfy both the conditions.
Diagrammatic representation:

Now, let us write the interval notation,
In interval notation, the symbol “$\in$” indicates that $x$ is included in that interval.
Rounded brackets in interval notation means that the value beside the bracket is not included in that set but everything up to that value is included.
A square bracket in interval notation indicates that the value beside the bracket is included in that set and everything up to that value is also included.
Note that the infinite values are always not included.
By using the above symbols and their uses, we can write the interval notation for the given question.
The given question is $x < 5$ and $x < 3$
As we have already discussed above, the $x$ value will be less than $3$ and goes on till negative infinity.
Therefore, interval is $x\in \left( -\infty ,3 \right)$
Interval notation for the given question is $x\in \left( -\infty ,3 \right)$.

Note: We should be well aware of the symbols which we use in the interval notation. Also, we should be well known about the usage of the symbols which we use in the interval notation. Also, we should be careful while finding the interval by using the given conditions in the given question. Also, we should be very careful while writing the interval.