Let's go through the simplification process step by step for the expression [tex]\(21 + 6(n-1)\)[/tex].
1. Distribute the term [tex]\(6\)[/tex] within the parentheses:
Begin by applying the distributive property, which states [tex]\(a(b + c) = ab + ac\)[/tex], to the term [tex]\(6(n-1)\)[/tex]:
[tex]\[
6(n-1) = 6 \cdot n + 6 \cdot (-1)
\][/tex]
Simplifying the multiplication inside the parentheses, we get:
[tex]\[
6(n-1) = 6n - 6
\][/tex]
2. Substitute back into the original expression:
Now, substitute [tex]\(6n - 6\)[/tex] back into the original expression [tex]\(21 + 6(n-1)\)[/tex]:
[tex]\[
21 + 6(n-1) = 21 + (6n - 6)
\][/tex]
3. Combine like terms:
Combine the constant terms [tex]\(21\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
21 + (6n - 6) = 21 - 6 + 6n
\][/tex]
Simplify this further by performing the arithmetic operation on the constants:
[tex]\[
21 - 6 = 15
\][/tex]
Thus, we have:
[tex]\[
21 + 6(n-1) = 15 + 6n
\][/tex]
Therefore, the simplified form of the given expression [tex]\(21 + 6(n-1)\)[/tex] is:
[tex]\[
6n + 15
\][/tex]
