To determine which of the given expressions is not equivalent to [tex]\( 15n + 10 \)[/tex], we need to simplify each expression and compare the results.
Expression 1:
[tex]\[ 5(3n + 2) \][/tex]
First, distribute the 5:
[tex]\[ 5 \cdot 3n + 5 \cdot 2 = 15n + 10 \][/tex]
Expression 2:
[tex]\[ 10n + 10 + 5n \][/tex]
Combine the like terms (terms containing [tex]\( n \)[/tex] and constants):
[tex]\[ 10n + 5n + 10 = 15n + 10 \][/tex]
Expression 3:
[tex]\[ 15n + 15 - 5 \][/tex]
Combine the constant terms:
[tex]\[ 15n + (15 - 5) = 15n + 10 \][/tex]
Expression 4:
[tex]\[ 8n + 8 + 7n + 7 \][/tex]
Combine the like terms:
[tex]\[ (8n + 7n) + (8 + 7) = 15n + 15 \][/tex]
This simplifies to:
[tex]\[ 15n + 15 \][/tex]
Upon comparing all the simplified expressions with [tex]\( 15n + 10 \)[/tex], we see that Expression 4, [tex]\( 8n + 8 + 7n + 7 \)[/tex], simplifies to [tex]\( 15n + 15 \)[/tex], which is not equivalent to [tex]\( 15n + 10 \)[/tex].
Therefore, the expression that is not equivalent to [tex]\( 15n + 10 \)[/tex] is:
[tex]\[ \boxed{4} \][/tex]
