Question

How do you write the expression for all real numbers that are less than 6 and greater than 2?

Answer 1

Hint: We are given to write an algebraic expression for all real numbers that are less than 6 and greater than 2. So, therefore we have to divide the given statement into 2 parts and we have to find the algebraic expressions for two parts separately and we have to combine them for the final algebraic expression.

Complete step by step answer:
For the given problem we have to find an algebraic expression for the statement “All real numbers that are less than 6 and greater than 2”.
So, let us assume that a given statement is a statement (1).
Let us consider,
All real numbers that are less than 6 and greater than 2\[............statement\left( 1 \right)\].
If we observe statement (1) it is clear that we have to find an algebraic expression for that equation.
Let us divide statement (2) into two parts,
Let us consider,
All real numbers that are less than 6\[............statement\left( 2 \right)\].
All real numbers that are greater than 2\[............statement\left( 3 \right)\].
The algebraic expression for statement (2) is
\[x<6\]
Let us consider the above equation as equation (1).
\[x<6.........equation(1)\]
The algebraic expression for statement (2).
\[x>2\]
Let us consider the above equation as equation (2)
\[x>2........equation(2)\]
By combining equation (1) and equation (2) we will get our final algebraic expression.
Combining equation (1) and (2), we get
\[2 < x < 6\]
Let us consider
\[2 < x < 6............equation(3)\]
Therefore \[2 < x < 6\] is the algebraic expression for all real numbers that are less than 6 and greater than 2.

Note:
 Students should have a keen knowledge of the inequalities concept to solve this question. Students should not confuse inequality symbols i.e. (<, >). We can do this problem in many other methods like the number line method, set builder method, etc. In all these methods this method is simple and easy to understand.