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Simplifying 8(7 + 5n) + -6(1 + -3n) = 5n + -7 + -2n + 2 (7 * 8 + 5n * 8) + -6(1 + -3n) = 5n + -7 + -2n + 2 (56 + 40n) + -6(1 + -3n) = 5n + -7 + -2n + 2 56 + 40n + (1 * -6 + -3n * -6) = 5n + -7 + -2n + 2 56 + 40n + (-6 + 18n) = 5n + -7 + -2n + 2 Reorder the terms: 56 + -6 + 40n + 18n = 5n + -7 + -2n + 2 Combine like terms: 56 + -6 = 50 50 + 40n + 18n = 5n + -7 + -2n + 2 Combine like terms: 40n + 18n = 58n 50 + 58n = 5n + -7 + -2n + 2 Reorder the terms: 50 + 58n = -7 + 2 + 5n + -2n Combine like terms: -7 + 2 = -5 50 + 58n = -5 + 5n + -2n Combine like terms: 5n + -2n = 3n 50 + 58n = -5 + 3n Solving 50 + 58n = -5 + 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. 50 + 58n + -3n = -5 + 3n + -3n Combine like terms: 58n + -3n = 55n 50 + 55n = -5 + 3n + -3n Combine like terms: 3n + -3n = 0 50 + 55n = -5 + 0 50 + 55n = -5 Add '-50' to each side of the equation. 50 + -50 + 55n = -5 + -50 Combine like terms: 50 + -50 = 0 0 + 55n = -5 + -50 55n = -5 + -50 Combine like terms: -5 + -50 = -55 55n = -55 Divide each side by '55'. n = -1 Simplifying n = -1
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