Question

How do you express intervals as inequalities such as \[[3,8)\] ?

Answer 1

Hint: Here we have interval notation. Interval notation is a simplified form of writing the solution to an inequality or system of inequality using brackets and parentheses symbols. An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. We need to express the given interval notation two inequality notation that is in the form containing the symbols \[ < , = , > \]

Complete step-by-step answer:
Given, \[[3,8)\]
Intervals with parentheses are called open intervals, meaning that the variable cannot have the value of the endpoints. Similarly intervals with brackets are called closed intervals, meaning that the variable can have the value of the endpoint.
Now, \[[3,8)\] , let ‘x’ be a some variable such that
 \[ \Rightarrow 3 \leqslant x < 8\] .
(The meaning if the above inequality is ‘x’ takes the value greater than or equal to 3 and ‘x’ also takes all the values is less than ‘8’)

Note: let’s say that they asked us to express the inequality form into interval notation.We have \[3 \leqslant x < 8\] ,As we have explained earlier in above we can directly write it as \[x \in [3,8)\] . Note that when performing algebraic operations on inequalities, it is important to perform the same operation on both sides in order to preserve the truth of the statement.