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Simplifying n + 4 + 1 + 10n = -1(n + 1) + 6(n + -3) Reorder the terms: 4 + 1 + n + 10n = -1(n + 1) + 6(n + -3) Combine like terms: 4 + 1 = 5 5 + n + 10n = -1(n + 1) + 6(n + -3) Combine like terms: n + 10n = 11n 5 + 11n = -1(n + 1) + 6(n + -3) Reorder the terms: 5 + 11n = -1(1 + n) + 6(n + -3) 5 + 11n = (1 * -1 + n * -1) + 6(n + -3) 5 + 11n = (-1 + -1n) + 6(n + -3) Reorder the terms: 5 + 11n = -1 + -1n + 6(-3 + n) 5 + 11n = -1 + -1n + (-3 * 6 + n * 6) 5 + 11n = -1 + -1n + (-18 + 6n) Reorder the terms: 5 + 11n = -1 + -18 + -1n + 6n Combine like terms: -1 + -18 = -19 5 + 11n = -19 + -1n + 6n Combine like terms: -1n + 6n = 5n 5 + 11n = -19 + 5n Solving 5 + 11n = -19 + 5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5n' to each side of the equation. 5 + 11n + -5n = -19 + 5n + -5n Combine like terms: 11n + -5n = 6n 5 + 6n = -19 + 5n + -5n Combine like terms: 5n + -5n = 0 5 + 6n = -19 + 0 5 + 6n = -19 Add '-5' to each side of the equation. 5 + -5 + 6n = -19 + -5 Combine like terms: 5 + -5 = 0 0 + 6n = -19 + -5 6n = -19 + -5 Combine like terms: -19 + -5 = -24 6n = -24 Divide each side by '6'. n = -4 Simplifying n = -4
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