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Solve for [tex]\( n \)[/tex].

[tex]\[ 11(n-1) + 35 = 3n \][/tex]

A. [tex]\( n = -6 \)[/tex]

B. [tex]\( n = -3 \)[/tex]

C. [tex]\( n = 3 \)[/tex]

D. [tex]\( n = 6 \)[/tex]

Sagot :

GinnyAnswer
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]
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