3(n-1)-2=4(n-4)+(n-11)

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Solution for 3(n-1)-2=4(n-4)+(n-11) equation:


Simplifying
3(n + -1) + -2 = 4(n + -4) + (n + -11)

Reorder the terms:
3(-1 + n) + -2 = 4(n + -4) + (n + -11)
(-1 * 3 + n * 3) + -2 = 4(n + -4) + (n + -11)
(-3 + 3n) + -2 = 4(n + -4) + (n + -11)

Reorder the terms:
-3 + -2 + 3n = 4(n + -4) + (n + -11)

Combine like terms: -3 + -2 = -5
-5 + 3n = 4(n + -4) + (n + -11)

Reorder the terms:
-5 + 3n = 4(-4 + n) + (n + -11)
-5 + 3n = (-4 * 4 + n * 4) + (n + -11)
-5 + 3n = (-16 + 4n) + (n + -11)

Reorder the terms:
-5 + 3n = -16 + 4n + (-11 + n)

Remove parenthesis around (-11 + n)
-5 + 3n = -16 + 4n + -11 + n

Reorder the terms:
-5 + 3n = -16 + -11 + 4n + n

Combine like terms: -16 + -11 = -27
-5 + 3n = -27 + 4n + n

Combine like terms: 4n + n = 5n
-5 + 3n = -27 + 5n

Solving
-5 + 3n = -27 + 5n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-5n' to each side of the equation.
-5 + 3n + -5n = -27 + 5n + -5n

Combine like terms: 3n + -5n = -2n
-5 + -2n = -27 + 5n + -5n

Combine like terms: 5n + -5n = 0
-5 + -2n = -27 + 0
-5 + -2n = -27

Add '5' to each side of the equation.
-5 + 5 + -2n = -27 + 5

Combine like terms: -5 + 5 = 0
0 + -2n = -27 + 5
-2n = -27 + 5

Combine like terms: -27 + 5 = -22
-2n = -22

Divide each side by '-2'.
n = 11

Simplifying
n = 11

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