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If an integer a is greater 7, then \[\left| 7-a \right|\] is
A. \[7-a\]
B. \[a-7\]
C. \[7+a\]
D. \[-7-a\]

Last updated date: 12th Jul 2024
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Hint: We have to solve this question using integers concept. To solve this question first we will derive the equation from the statement given and then we use that equation to solve the given expression. We have to simplify it until we arrive at the solution.

Complete step-by-step answer:

Given that A is greater than 7.
As a is greater than 7 if we subtract 7 from a we will get a positive number.
So we can write
\[a-7>0....\left( 1 \right)\]
Now we will take the expression given to find the value.
It is asked the value of \[\left| 7-a \right|\].
we can rewrite it as
\[\Rightarrow \left| -a+7 \right|\]
Now we will multiply the expression inside the mod with -. We will get
\[\Rightarrow \left| -\left( -a+7 \right) \right|\]
By simplifying it we will get
\[\Rightarrow \left| a-7 \right|\]
Now we can rewrite the expression using equation 1.
In equation 1 we derived that \[a-7>0\].
So we can say \[a-7\] is a positive integer.
We already know that mod of a positive integer is itself.
So we can use this to solve the expression we have derived.
Using equation 1 we can write
\[\Rightarrow a-7\]
So if the integer a is greater than 7 and then the value of \[\left| 7-a \right|\] is \[a-7\].
The answer is \[option\left( B \right)\].
So, the correct answer is “Option B”.

Note: We should be careful while deriving the given expression. There is a chance we can change the symbol while rewriting or deriving. If we change any symbol then we will get a wrong answer. We have to be aware of modulus formulas.