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Simplifying -6 + -4n + 5n + -5 = -1(1 + 3n) + -7(-8 + n) Reorder the terms: -6 + -5 + -4n + 5n = -1(1 + 3n) + -7(-8 + n) Combine like terms: -6 + -5 = -11 -11 + -4n + 5n = -1(1 + 3n) + -7(-8 + n) Combine like terms: -4n + 5n = 1n -11 + 1n = -1(1 + 3n) + -7(-8 + n) -11 + 1n = (1 * -1 + 3n * -1) + -7(-8 + n) -11 + 1n = (-1 + -3n) + -7(-8 + n) -11 + 1n = -1 + -3n + (-8 * -7 + n * -7) -11 + 1n = -1 + -3n + (56 + -7n) Reorder the terms: -11 + 1n = -1 + 56 + -3n + -7n Combine like terms: -1 + 56 = 55 -11 + 1n = 55 + -3n + -7n Combine like terms: -3n + -7n = -10n -11 + 1n = 55 + -10n Solving -11 + 1n = 55 + -10n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '10n' to each side of the equation. -11 + 1n + 10n = 55 + -10n + 10n Combine like terms: 1n + 10n = 11n -11 + 11n = 55 + -10n + 10n Combine like terms: -10n + 10n = 0 -11 + 11n = 55 + 0 -11 + 11n = 55 Add '11' to each side of the equation. -11 + 11 + 11n = 55 + 11 Combine like terms: -11 + 11 = 0 0 + 11n = 55 + 11 11n = 55 + 11 Combine like terms: 55 + 11 = 66 11n = 66 Divide each side by '11'. n = 6 Simplifying n = 6
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