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Simplifying -13 + 10n + -30 = -1(1 + -16n) + -5(n + 20) Reorder the terms: -13 + -30 + 10n = -1(1 + -16n) + -5(n + 20) Combine like terms: -13 + -30 = -43 -43 + 10n = -1(1 + -16n) + -5(n + 20) -43 + 10n = (1 * -1 + -16n * -1) + -5(n + 20) -43 + 10n = (-1 + 16n) + -5(n + 20) Reorder the terms: -43 + 10n = -1 + 16n + -5(20 + n) -43 + 10n = -1 + 16n + (20 * -5 + n * -5) -43 + 10n = -1 + 16n + (-100 + -5n) Reorder the terms: -43 + 10n = -1 + -100 + 16n + -5n Combine like terms: -1 + -100 = -101 -43 + 10n = -101 + 16n + -5n Combine like terms: 16n + -5n = 11n -43 + 10n = -101 + 11n Solving -43 + 10n = -101 + 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. -43 + 10n + -11n = -101 + 11n + -11n Combine like terms: 10n + -11n = -1n -43 + -1n = -101 + 11n + -11n Combine like terms: 11n + -11n = 0 -43 + -1n = -101 + 0 -43 + -1n = -101 Add '43' to each side of the equation. -43 + 43 + -1n = -101 + 43 Combine like terms: -43 + 43 = 0 0 + -1n = -101 + 43 -1n = -101 + 43 Combine like terms: -101 + 43 = -58 -1n = -58 Divide each side by '-1'. n = 58 Simplifying n = 58
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