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Simplifying -12(n + 3) + 2 = 6(n + -1) + 8 Reorder the terms: -12(3 + n) + 2 = 6(n + -1) + 8 (3 * -12 + n * -12) + 2 = 6(n + -1) + 8 (-36 + -12n) + 2 = 6(n + -1) + 8 Reorder the terms: -36 + 2 + -12n = 6(n + -1) + 8 Combine like terms: -36 + 2 = -34 -34 + -12n = 6(n + -1) + 8 Reorder the terms: -34 + -12n = 6(-1 + n) + 8 -34 + -12n = (-1 * 6 + n * 6) + 8 -34 + -12n = (-6 + 6n) + 8 Reorder the terms: -34 + -12n = -6 + 8 + 6n Combine like terms: -6 + 8 = 2 -34 + -12n = 2 + 6n Solving -34 + -12n = 2 + 6n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6n' to each side of the equation. -34 + -12n + -6n = 2 + 6n + -6n Combine like terms: -12n + -6n = -18n -34 + -18n = 2 + 6n + -6n Combine like terms: 6n + -6n = 0 -34 + -18n = 2 + 0 -34 + -18n = 2 Add '34' to each side of the equation. -34 + 34 + -18n = 2 + 34 Combine like terms: -34 + 34 = 0 0 + -18n = 2 + 34 -18n = 2 + 34 Combine like terms: 2 + 34 = 36 -18n = 36 Divide each side by '-18'. n = -2 Simplifying n = -2
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