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Simplifying 2[7 + -4(1 + -1n)] + 4n = -10 + 3[6(n + 1) + -3n] 2[7 + (1 * -4 + -1n * -4)] + 4n = -10 + 3[6(n + 1) + -3n] 2[7 + (-4 + 4n)] + 4n = -10 + 3[6(n + 1) + -3n] Combine like terms: 7 + -4 = 3 2[3 + 4n] + 4n = -10 + 3[6(n + 1) + -3n] [3 * 2 + 4n * 2] + 4n = -10 + 3[6(n + 1) + -3n] [6 + 8n] + 4n = -10 + 3[6(n + 1) + -3n] Combine like terms: 8n + 4n = 12n 6 + 12n = -10 + 3[6(n + 1) + -3n] Reorder the terms: 6 + 12n = -10 + 3[6(1 + n) + -3n] 6 + 12n = -10 + 3[(1 * 6 + n * 6) + -3n] 6 + 12n = -10 + 3[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 6 + 12n = -10 + 3[6 + 3n] 6 + 12n = -10 + [6 * 3 + 3n * 3] 6 + 12n = -10 + [18 + 9n] Combine like terms: -10 + 18 = 8 6 + 12n = 8 + 9n Solving 6 + 12n = 8 + 9n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9n' to each side of the equation. 6 + 12n + -9n = 8 + 9n + -9n Combine like terms: 12n + -9n = 3n 6 + 3n = 8 + 9n + -9n Combine like terms: 9n + -9n = 0 6 + 3n = 8 + 0 6 + 3n = 8 Add '-6' to each side of the equation. 6 + -6 + 3n = 8 + -6 Combine like terms: 6 + -6 = 0 0 + 3n = 8 + -6 3n = 8 + -6 Combine like terms: 8 + -6 = 2 3n = 2 Divide each side by '3'. n = 0.6666666667 Simplifying n = 0.6666666667
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