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Simplifying -27 = 7(4n + 1) + -2(1 + -2n) Reorder the terms: -27 = 7(1 + 4n) + -2(1 + -2n) -27 = (1 * 7 + 4n * 7) + -2(1 + -2n) -27 = (7 + 28n) + -2(1 + -2n) -27 = 7 + 28n + (1 * -2 + -2n * -2) -27 = 7 + 28n + (-2 + 4n) Reorder the terms: -27 = 7 + -2 + 28n + 4n Combine like terms: 7 + -2 = 5 -27 = 5 + 28n + 4n Combine like terms: 28n + 4n = 32n -27 = 5 + 32n Solving -27 = 5 + 32n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-32n' to each side of the equation. -27 + -32n = 5 + 32n + -32n Combine like terms: 32n + -32n = 0 -27 + -32n = 5 + 0 -27 + -32n = 5 Add '27' to each side of the equation. -27 + 27 + -32n = 5 + 27 Combine like terms: -27 + 27 = 0 0 + -32n = 5 + 27 -32n = 5 + 27 Combine like terms: 5 + 27 = 32 -32n = 32 Divide each side by '-32'. n = -1 Simplifying n = -1
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