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Simplifying 12n + -2 + 4n = -2(n + -12) + 8(3n + 11) Reorder the terms: -2 + 12n + 4n = -2(n + -12) + 8(3n + 11) Combine like terms: 12n + 4n = 16n -2 + 16n = -2(n + -12) + 8(3n + 11) Reorder the terms: -2 + 16n = -2(-12 + n) + 8(3n + 11) -2 + 16n = (-12 * -2 + n * -2) + 8(3n + 11) -2 + 16n = (24 + -2n) + 8(3n + 11) Reorder the terms: -2 + 16n = 24 + -2n + 8(11 + 3n) -2 + 16n = 24 + -2n + (11 * 8 + 3n * 8) -2 + 16n = 24 + -2n + (88 + 24n) Reorder the terms: -2 + 16n = 24 + 88 + -2n + 24n Combine like terms: 24 + 88 = 112 -2 + 16n = 112 + -2n + 24n Combine like terms: -2n + 24n = 22n -2 + 16n = 112 + 22n Solving -2 + 16n = 112 + 22n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-22n' to each side of the equation. -2 + 16n + -22n = 112 + 22n + -22n Combine like terms: 16n + -22n = -6n -2 + -6n = 112 + 22n + -22n Combine like terms: 22n + -22n = 0 -2 + -6n = 112 + 0 -2 + -6n = 112 Add '2' to each side of the equation. -2 + 2 + -6n = 112 + 2 Combine like terms: -2 + 2 = 0 0 + -6n = 112 + 2 -6n = 112 + 2 Combine like terms: 112 + 2 = 114 -6n = 114 Divide each side by '-6'. n = -19 Simplifying n = -19
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