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Simplifying 2[7 + -5(1 + -1n)] + 8n = -16 + 2[6(n + 1)] 2[7 + (1 * -5 + -1n * -5)] + 8n = -16 + 2[6(n + 1)] 2[7 + (-5 + 5n)] + 8n = -16 + 2[6(n + 1)] Combine like terms: 7 + -5 = 2 2[2 + 5n] + 8n = -16 + 2[6(n + 1)] [2 * 2 + 5n * 2] + 8n = -16 + 2[6(n + 1)] [4 + 10n] + 8n = -16 + 2[6(n + 1)] Combine like terms: 10n + 8n = 18n 4 + 18n = -16 + 2[6(n + 1)] Reorder the terms: 4 + 18n = -16 + 2[6(1 + n)] 4 + 18n = -16 + 2[(1 * 6 + n * 6)] 4 + 18n = -16 + 2[(6 + 6n)] 4 + 18n = -16 + [6 * 2 + 6n * 2] 4 + 18n = -16 + [12 + 12n] Combine like terms: -16 + 12 = -4 4 + 18n = -4 + 12n Solving 4 + 18n = -4 + 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. 4 + 18n + -12n = -4 + 12n + -12n Combine like terms: 18n + -12n = 6n 4 + 6n = -4 + 12n + -12n Combine like terms: 12n + -12n = 0 4 + 6n = -4 + 0 4 + 6n = -4 Add '-4' to each side of the equation. 4 + -4 + 6n = -4 + -4 Combine like terms: 4 + -4 = 0 0 + 6n = -4 + -4 6n = -4 + -4 Combine like terms: -4 + -4 = -8 6n = -8 Divide each side by '6'. n = -1.333333333 Simplifying n = -1.333333333
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