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Simplifying 2[7 + -6(1 + -1n)] + 5 = -8 + 2[6(n + 1) + -3n] 2[7 + (1 * -6 + -1n * -6)] + 5 = -8 + 2[6(n + 1) + -3n] 2[7 + (-6 + 6n)] + 5 = -8 + 2[6(n + 1) + -3n] Combine like terms: 7 + -6 = 1 2[1 + 6n] + 5 = -8 + 2[6(n + 1) + -3n] [1 * 2 + 6n * 2] + 5 = -8 + 2[6(n + 1) + -3n] [2 + 12n] + 5 = -8 + 2[6(n + 1) + -3n] Reorder the terms: 2 + 5 + 12n = -8 + 2[6(n + 1) + -3n] Combine like terms: 2 + 5 = 7 7 + 12n = -8 + 2[6(n + 1) + -3n] Reorder the terms: 7 + 12n = -8 + 2[6(1 + n) + -3n] 7 + 12n = -8 + 2[(1 * 6 + n * 6) + -3n] 7 + 12n = -8 + 2[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 7 + 12n = -8 + 2[6 + 3n] 7 + 12n = -8 + [6 * 2 + 3n * 2] 7 + 12n = -8 + [12 + 6n] Combine like terms: -8 + 12 = 4 7 + 12n = 4 + 6n Solving 7 + 12n = 4 + 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. 7 + 12n + -6n = 4 + 6n + -6n Combine like terms: 12n + -6n = 6n 7 + 6n = 4 + 6n + -6n Combine like terms: 6n + -6n = 0 7 + 6n = 4 + 0 7 + 6n = 4 Add '-7' to each side of the equation. 7 + -7 + 6n = 4 + -7 Combine like terms: 7 + -7 = 0 0 + 6n = 4 + -7 6n = 4 + -7 Combine like terms: 4 + -7 = -3 6n = -3 Divide each side by '6'. n = -0.5 Simplifying n = -0.5
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