2[7-1(1-n)]+5n=-22+4[6(n+1)-3n]

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Solution for 2[7-1(1-n)]+5n=-22+4[6(n+1)-3n] equation:


Simplifying
2[7 + -1(1 + -1n)] + 5n = -22 + 4[6(n + 1) + -3n]
2[7 + (1 * -1 + -1n * -1)] + 5n = -22 + 4[6(n + 1) + -3n]
2[7 + (-1 + 1n)] + 5n = -22 + 4[6(n + 1) + -3n]

Combine like terms: 7 + -1 = 6
2[6 + 1n] + 5n = -22 + 4[6(n + 1) + -3n]
[6 * 2 + 1n * 2] + 5n = -22 + 4[6(n + 1) + -3n]
[12 + 2n] + 5n = -22 + 4[6(n + 1) + -3n]

Combine like terms: 2n + 5n = 7n
12 + 7n = -22 + 4[6(n + 1) + -3n]

Reorder the terms:
12 + 7n = -22 + 4[6(1 + n) + -3n]
12 + 7n = -22 + 4[(1 * 6 + n * 6) + -3n]
12 + 7n = -22 + 4[(6 + 6n) + -3n]

Combine like terms: 6n + -3n = 3n
12 + 7n = -22 + 4[6 + 3n]
12 + 7n = -22 + [6 * 4 + 3n * 4]
12 + 7n = -22 + [24 + 12n]

Combine like terms: -22 + 24 = 2
12 + 7n = 2 + 12n

Solving
12 + 7n = 2 + 12n

Solving for variable 'n'.

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

Add '-12n' to each side of the equation.
12 + 7n + -12n = 2 + 12n + -12n

Combine like terms: 7n + -12n = -5n
12 + -5n = 2 + 12n + -12n

Combine like terms: 12n + -12n = 0
12 + -5n = 2 + 0
12 + -5n = 2

Add '-12' to each side of the equation.
12 + -12 + -5n = 2 + -12

Combine like terms: 12 + -12 = 0
0 + -5n = 2 + -12
-5n = 2 + -12

Combine like terms: 2 + -12 = -10
-5n = -10

Divide each side by '-5'.
n = 2

Simplifying
n = 2

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