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Simplifying 2[7 + -4(1 + -1n)] + 7n = 4 + 2[6(n + 1) + -3n] 2[7 + (1 * -4 + -1n * -4)] + 7n = 4 + 2[6(n + 1) + -3n] 2[7 + (-4 + 4n)] + 7n = 4 + 2[6(n + 1) + -3n] Combine like terms: 7 + -4 = 3 2[3 + 4n] + 7n = 4 + 2[6(n + 1) + -3n] [3 * 2 + 4n * 2] + 7n = 4 + 2[6(n + 1) + -3n] [6 + 8n] + 7n = 4 + 2[6(n + 1) + -3n] Combine like terms: 8n + 7n = 15n 6 + 15n = 4 + 2[6(n + 1) + -3n] Reorder the terms: 6 + 15n = 4 + 2[6(1 + n) + -3n] 6 + 15n = 4 + 2[(1 * 6 + n * 6) + -3n] 6 + 15n = 4 + 2[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 6 + 15n = 4 + 2[6 + 3n] 6 + 15n = 4 + [6 * 2 + 3n * 2] 6 + 15n = 4 + [12 + 6n] Combine like terms: 4 + 12 = 16 6 + 15n = 16 + 6n Solving 6 + 15n = 16 + 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. 6 + 15n + -6n = 16 + 6n + -6n Combine like terms: 15n + -6n = 9n 6 + 9n = 16 + 6n + -6n Combine like terms: 6n + -6n = 0 6 + 9n = 16 + 0 6 + 9n = 16 Add '-6' to each side of the equation. 6 + -6 + 9n = 16 + -6 Combine like terms: 6 + -6 = 0 0 + 9n = 16 + -6 9n = 16 + -6 Combine like terms: 16 + -6 = 10 9n = 10 Divide each side by '9'. n = 1.111111111 Simplifying n = 1.111111111
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