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Simplifying 3[8 + -4(n + -2)] + 5n = -20 + 2[5(1 + -1n) + -6n] Reorder the terms: 3[8 + -4(-2 + n)] + 5n = -20 + 2[5(1 + -1n) + -6n] 3[8 + (-2 * -4 + n * -4)] + 5n = -20 + 2[5(1 + -1n) + -6n] 3[8 + (8 + -4n)] + 5n = -20 + 2[5(1 + -1n) + -6n] Combine like terms: 8 + 8 = 16 3[16 + -4n] + 5n = -20 + 2[5(1 + -1n) + -6n] [16 * 3 + -4n * 3] + 5n = -20 + 2[5(1 + -1n) + -6n] [48 + -12n] + 5n = -20 + 2[5(1 + -1n) + -6n] Combine like terms: -12n + 5n = -7n 48 + -7n = -20 + 2[5(1 + -1n) + -6n] 48 + -7n = -20 + 2[(1 * 5 + -1n * 5) + -6n] 48 + -7n = -20 + 2[(5 + -5n) + -6n] Combine like terms: -5n + -6n = -11n 48 + -7n = -20 + 2[5 + -11n] 48 + -7n = -20 + [5 * 2 + -11n * 2] 48 + -7n = -20 + [10 + -22n] Combine like terms: -20 + 10 = -10 48 + -7n = -10 + -22n Solving 48 + -7n = -10 + -22n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '22n' to each side of the equation. 48 + -7n + 22n = -10 + -22n + 22n Combine like terms: -7n + 22n = 15n 48 + 15n = -10 + -22n + 22n Combine like terms: -22n + 22n = 0 48 + 15n = -10 + 0 48 + 15n = -10 Add '-48' to each side of the equation. 48 + -48 + 15n = -10 + -48 Combine like terms: 48 + -48 = 0 0 + 15n = -10 + -48 15n = -10 + -48 Combine like terms: -10 + -48 = -58 15n = -58 Divide each side by '15'. n = -3.866666667 Simplifying n = -3.866666667
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