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Simplifying -37 = 5(4n + 6) + -1(9n + 1) Reorder the terms: -37 = 5(6 + 4n) + -1(9n + 1) -37 = (6 * 5 + 4n * 5) + -1(9n + 1) -37 = (30 + 20n) + -1(9n + 1) Reorder the terms: -37 = 30 + 20n + -1(1 + 9n) -37 = 30 + 20n + (1 * -1 + 9n * -1) -37 = 30 + 20n + (-1 + -9n) Reorder the terms: -37 = 30 + -1 + 20n + -9n Combine like terms: 30 + -1 = 29 -37 = 29 + 20n + -9n Combine like terms: 20n + -9n = 11n -37 = 29 + 11n Solving -37 = 29 + 11n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11n' to each side of the equation. -37 + -11n = 29 + 11n + -11n Combine like terms: 11n + -11n = 0 -37 + -11n = 29 + 0 -37 + -11n = 29 Add '37' to each side of the equation. -37 + 37 + -11n = 29 + 37 Combine like terms: -37 + 37 = 0 0 + -11n = 29 + 37 -11n = 29 + 37 Combine like terms: 29 + 37 = 66 -11n = 66 Divide each side by '-11'. n = -6 Simplifying n = -6
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