Question

How do you express “two less than a number is less than 9” as an equation.

Answer 1

Hint: The above-given statement basically describes inequality. We can break the above-given statement into two parts. The first part says that “two less than a number” so let us describe it as $ A $. And, the second part says that “A is less than 9” so we can write it A<9. Since A is “two less than a number” so let us say that number is ‘x’ then 2 less than ‘x’ can be written as (x-2) so we can say that x -2 < 9. Thus, x < 11 will be our answer.

Complete step by step answer:
We will use the concept of inequality to solve the above question because the question does not say that two things are equal but it says that something is “less than” something else.
So, when we have the statement like “A is less than B” then we write it in mathematical form as
A < B.
We can see that question describes the statement “two less than a number is less than 9”. So, we can say that let A describe the statement “two less than a number”. Then, we have statements like “A is less than 9”.
So, we can express the above statement “A is less than 9” as A < 9.
Now, we will try to mathematically express A.
A = two less than a number.
Let us assume that the number is ‘x’.
So, we can write “2 less than x” equal to (x – 2).
This implies that statement A is equivalent to (x – 2).
Now, we have “A is less than 9” as A < 9. So, we can write it as (x – 2 ) < 9.
 $ \Rightarrow x-2<9 $
This is the required expression of the above-given statement.
Now, we can also simplify it in the following ways:
We will add 2 on both sides of the inequality then we will get:
  $ \Rightarrow x-2+2<9+2 $
 $ \Rightarrow x<11 $
So, the statement “two less than a number is less than 9” is equivalent to $ x<11 $.

Note:
 When we are given a statement that is to be expressed in the mathematical form then we are required to split the given statement into two or three possible parts and then we are required to first express each part of the statement into mathematical and then we are required to combine all of them to get the required equation.