Question

How do you solve and write the following in interval notation: $-1 < x < 5$?

Answer 1

Hint: The given interval for variable x is for $-1 < x < 5$. We explain the domain of the variable. We also explain the open and closed interval part. We try to express the interval thing in other ways also.

Complete step by step answer:
The given interval of x is $-1 < x < 5$. The domain of the variable is the real part.
The form $-1 < x < 5$ means that the value of x will be greater than -1 and less than 5.
This expression can also be expressed in other ways.
The use of brackets which explains the boundary. The use of ‘$\left( {} \right)$’ is for open boundary and the use of ‘$\left[ {} \right]$’ is for closed boundary.
The open boundary is used when we don’t include the boundary point and the closed boundary is used when we include the boundary point.
For our given interval x can never be equal to -1 or 5. This means we can include neither -1 nor 5.
The interval will be an open interval. The other expression for $-1 < x < 5$ will be $x\in \left( -1,5 \right)$.

We can also express as the complementary interval where $x\in \left( -1,5 \right)$.

Note: The interval is given for a real valued function where the variable does not belong in the imaginary part. That’s why we only used the notation of $\mathbb{R}$. Also, in case of imaginary intervals the respective values cannot be compared.