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Simplifying 2[7 + -7(1 + -1n)] + 3n = -10 + 2[6(n + 1) + -3n] 2[7 + (1 * -7 + -1n * -7)] + 3n = -10 + 2[6(n + 1) + -3n] 2[7 + (-7 + 7n)] + 3n = -10 + 2[6(n + 1) + -3n] Combine like terms: 7 + -7 = 0 2[0 + 7n] + 3n = -10 + 2[6(n + 1) + -3n] 2[7n] + 3n = -10 + 2[6(n + 1) + -3n] Remove brackets around [7n] 2 * 7n + 3n = -10 + 2[6(n + 1) + -3n] Multiply 2 * 7 14n + 3n = -10 + 2[6(n + 1) + -3n] Combine like terms: 14n + 3n = 17n 17n = -10 + 2[6(n + 1) + -3n] Reorder the terms: 17n = -10 + 2[6(1 + n) + -3n] 17n = -10 + 2[(1 * 6 + n * 6) + -3n] 17n = -10 + 2[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 17n = -10 + 2[6 + 3n] 17n = -10 + [6 * 2 + 3n * 2] 17n = -10 + [12 + 6n] Combine like terms: -10 + 12 = 2 17n = 2 + 6n Solving 17n = 2 + 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. 17n + -6n = 2 + 6n + -6n Combine like terms: 17n + -6n = 11n 11n = 2 + 6n + -6n Combine like terms: 6n + -6n = 0 11n = 2 + 0 11n = 2 Divide each side by '11'. n = 0.1818181818 Simplifying n = 0.1818181818
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