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Simplifying 2[7 + -3(1 + -1n)] + 7n = -2 + 2[6(n + 1) + -3n] 2[7 + (1 * -3 + -1n * -3)] + 7n = -2 + 2[6(n + 1) + -3n] 2[7 + (-3 + 3n)] + 7n = -2 + 2[6(n + 1) + -3n] Combine like terms: 7 + -3 = 4 2[4 + 3n] + 7n = -2 + 2[6(n + 1) + -3n] [4 * 2 + 3n * 2] + 7n = -2 + 2[6(n + 1) + -3n] [8 + 6n] + 7n = -2 + 2[6(n + 1) + -3n] Combine like terms: 6n + 7n = 13n 8 + 13n = -2 + 2[6(n + 1) + -3n] Reorder the terms: 8 + 13n = -2 + 2[6(1 + n) + -3n] 8 + 13n = -2 + 2[(1 * 6 + n * 6) + -3n] 8 + 13n = -2 + 2[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 8 + 13n = -2 + 2[6 + 3n] 8 + 13n = -2 + [6 * 2 + 3n * 2] 8 + 13n = -2 + [12 + 6n] Combine like terms: -2 + 12 = 10 8 + 13n = 10 + 6n Solving 8 + 13n = 10 + 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. 8 + 13n + -6n = 10 + 6n + -6n Combine like terms: 13n + -6n = 7n 8 + 7n = 10 + 6n + -6n Combine like terms: 6n + -6n = 0 8 + 7n = 10 + 0 8 + 7n = 10 Add '-8' to each side of the equation. 8 + -8 + 7n = 10 + -8 Combine like terms: 8 + -8 = 0 0 + 7n = 10 + -8 7n = 10 + -8 Combine like terms: 10 + -8 = 2 7n = 2 Divide each side by '7'. n = 0.2857142857 Simplifying n = 0.2857142857
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