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Simplifying 69 = 8(7n + -1) + -5(1 + 3n) Reorder the terms: 69 = 8(-1 + 7n) + -5(1 + 3n) 69 = (-1 * 8 + 7n * 8) + -5(1 + 3n) 69 = (-8 + 56n) + -5(1 + 3n) 69 = -8 + 56n + (1 * -5 + 3n * -5) 69 = -8 + 56n + (-5 + -15n) Reorder the terms: 69 = -8 + -5 + 56n + -15n Combine like terms: -8 + -5 = -13 69 = -13 + 56n + -15n Combine like terms: 56n + -15n = 41n 69 = -13 + 41n Solving 69 = -13 + 41n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-41n' to each side of the equation. 69 + -41n = -13 + 41n + -41n Combine like terms: 41n + -41n = 0 69 + -41n = -13 + 0 69 + -41n = -13 Add '-69' to each side of the equation. 69 + -69 + -41n = -13 + -69 Combine like terms: 69 + -69 = 0 0 + -41n = -13 + -69 -41n = -13 + -69 Combine like terms: -13 + -69 = -82 -41n = -82 Divide each side by '-41'. n = 2 Simplifying n = 2
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