To solve the equation [tex]\( 11(n - 1) + 35 = 3n \)[/tex] for [tex]\( n \)[/tex], follow these steps:
1. Expand the equation:
[tex]\[
11(n - 1) + 35 = 3n
\][/tex]
Distribute the [tex]\( 11 \)[/tex] inside the parentheses:
[tex]\[
11n - 11 + 35 = 3n
\][/tex]
2. Simplify the left side:
Combine the constants [tex]\(-11\)[/tex] and [tex]\(35\)[/tex]:
[tex]\[
11n + 24 = 3n
\][/tex]
3. Isolate the variable term:
Subtract [tex]\(3n\)[/tex] from both sides to get all the [tex]\(n\)[/tex] terms on one side:
[tex]\[
11n - 3n + 24 = 0
\][/tex]
Simplify by combining like terms:
[tex]\[
8n + 24 = 0
\][/tex]
4. Solve for [tex]\(n\)[/tex]:
Subtract [tex]\(24\)[/tex] from both sides to isolate the term containing [tex]\(n\)[/tex]:
[tex]\[
8n = -24
\][/tex]
Divide both sides by [tex]\(8\)[/tex]:
[tex]\[
n = -3
\][/tex]
Therefore, the solution to the equation [tex]\( 11(n - 1) + 35 = 3n \)[/tex] is:
[tex]\[
n = -3
\][/tex]
