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Simplifying 2[7 + -4(1 + -1n)] + 8n = -10 + 3[6(n + 1) + -3] 2[7 + (1 * -4 + -1n * -4)] + 8n = -10 + 3[6(n + 1) + -3] 2[7 + (-4 + 4n)] + 8n = -10 + 3[6(n + 1) + -3] Combine like terms: 7 + -4 = 3 2[3 + 4n] + 8n = -10 + 3[6(n + 1) + -3] [3 * 2 + 4n * 2] + 8n = -10 + 3[6(n + 1) + -3] [6 + 8n] + 8n = -10 + 3[6(n + 1) + -3] Combine like terms: 8n + 8n = 16n 6 + 16n = -10 + 3[6(n + 1) + -3] Reorder the terms: 6 + 16n = -10 + 3[6(1 + n) + -3] 6 + 16n = -10 + 3[(1 * 6 + n * 6) + -3] 6 + 16n = -10 + 3[(6 + 6n) + -3] Reorder the terms: 6 + 16n = -10 + 3[6 + -3 + 6n] Combine like terms: 6 + -3 = 3 6 + 16n = -10 + 3[3 + 6n] 6 + 16n = -10 + [3 * 3 + 6n * 3] 6 + 16n = -10 + [9 + 18n] Combine like terms: -10 + 9 = -1 6 + 16n = -1 + 18n Solving 6 + 16n = -1 + 18n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-18n' to each side of the equation. 6 + 16n + -18n = -1 + 18n + -18n Combine like terms: 16n + -18n = -2n 6 + -2n = -1 + 18n + -18n Combine like terms: 18n + -18n = 0 6 + -2n = -1 + 0 6 + -2n = -1 Add '-6' to each side of the equation. 6 + -6 + -2n = -1 + -6 Combine like terms: 6 + -6 = 0 0 + -2n = -1 + -6 -2n = -1 + -6 Combine like terms: -1 + -6 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5
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