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Simplifying -74 = 6(1 + -1n) + 7(1 + 5n) -74 = (1 * 6 + -1n * 6) + 7(1 + 5n) -74 = (6 + -6n) + 7(1 + 5n) -74 = 6 + -6n + (1 * 7 + 5n * 7) -74 = 6 + -6n + (7 + 35n) Reorder the terms: -74 = 6 + 7 + -6n + 35n Combine like terms: 6 + 7 = 13 -74 = 13 + -6n + 35n Combine like terms: -6n + 35n = 29n -74 = 13 + 29n Solving -74 = 13 + 29n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-29n' to each side of the equation. -74 + -29n = 13 + 29n + -29n Combine like terms: 29n + -29n = 0 -74 + -29n = 13 + 0 -74 + -29n = 13 Add '74' to each side of the equation. -74 + 74 + -29n = 13 + 74 Combine like terms: -74 + 74 = 0 0 + -29n = 13 + 74 -29n = 13 + 74 Combine like terms: 13 + 74 = 87 -29n = 87 Divide each side by '-29'. n = -3 Simplifying n = -3
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