Question

Express intervals as inequalities such as \[\left( -4,-2 \right)\]?

Answer 1

Hint: In this question we have to express the given interval \[\left( -4,-2 \right)\] as inequality so for that firstly we will consider an arbitrary number be \['n'\]. After that we will try to show that \['n'\] lies between the given interval that is \[\left( -4,-2 \right)\]. For inequality signs we have to check the breakers given in this question.

Complete step by step solution:
Let us assume the number be \['n'\] belongs to the given interval that is \[\left( -4,-2 \right)\].
This means that a number \['n'\] is lying between the given interval that is \[\left( -4,-2 \right)\].
Firstly we have to observe the brackets of the interval which is given in this question.
Here, we have parentheses that are \['\left(\,\,\, \right)'\].
This means that we do not have to include the end numbers of the given interval.
That is, we do not have to include \[-4\] and \[-2\] in inequality.
This means that the number \['n'\] is strictly greater than \[-4\] and strictly less than \[-2\].

Note: In order to express any intervals as inequality there are some key points which we have to always keep in mind white doing this. Those key points are mentioned below.
• If the interval is in brackets $[\,\,\,]$ then, This brackets means that we have to include both the numbers in inequality.
That is, If the interval is \[\left[ a,b \right]\] then this interval can be written as \[a\le x\le b\]. Which is a required form of inequality. Also we can read it as \[x\] is greater than or equal to \['a'\] and less than or equal to \['b'\].

• If we have given intervals in brackets $(\,\,\,)$. Then, this brackets means that we do not have to include both (end) numbers (that is we have to exclude both end that is, if we have given interval is \[\left( a,b \right)\] then this interval can be written as \[a < x < b\] which is required form of inequality.
Also, we can say \['x'\] is strictly greater than \['a'\] and strictly less than \['b'\].