A certain number [tex]$n$[/tex] is 6 more than a second number and 9 less than a third number. In terms of [tex]$n$[/tex], which of the following expressions represents the second number?

A. [tex]$n - 9$[/tex]
B. [tex]$n - 6$[/tex]
C. [tex]$n + 6$[/tex]
D. [tex]$n + 15$[/tex]



Answer :

Let's solve the problem step-by-step:

1. Understand the Given Information:
- We are given a certain number [tex]\( n \)[/tex].
- This number [tex]\( n \)[/tex] is 6 more than a second number.

2. Translate the Information into an Equation:
- Let the second number be represented as [tex]\( x \)[/tex].
- Since [tex]\( n \)[/tex] is 6 more than the second number [tex]\( x \)[/tex], we can write the relationship as:
[tex]\[ n = x + 6 \][/tex]

3. Isolate the Second Number [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex] in terms of [tex]\( n \)[/tex], we need to rearrange the equation:
[tex]\[ x = n - 6 \][/tex]

4. Conclusion:
- The expression for the second number in terms of [tex]\( n \)[/tex] is [tex]\( n - 6 \)[/tex].

So, the correct expression that represents the second number is [tex]\( \boxed{n - 6} \)[/tex].

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