To determine which expression is equivalent to the given expression [tex]\( n + 8n - 6n \)[/tex], we will combine the like terms step by step:
1. Identify the like terms: In the expression [tex]\( n + 8n - 6n \)[/tex], all terms involve the variable [tex]\( n \)[/tex].
2. Combine the coefficients: The coefficients of [tex]\( n \)[/tex] are 1 (from the term [tex]\( n \)[/tex]), 8 (from the term [tex]\( 8n \)[/tex]), and -6 (from the term [tex]\( -6n \)[/tex]).
3. Add the coefficients together:
[tex]\[
1 + 8 - 6
\][/tex]
4. Perform the addition and subtraction:
[tex]\[
1 + 8 = 9
\][/tex]
[tex]\[
9 - 6 = 3
\][/tex]
5. Write the equivalent expression: Since the combined coefficient is 3, the expression [tex]\( n + 8n - 6n \)[/tex] simplifies to [tex]\( 3n \)[/tex].
Therefore, the expression that is equivalent to [tex]\( n + 8n - 6n \)[/tex] is [tex]\( 3n \)[/tex].
