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Simplifying -3(n + -7) + 6(4 + 3n) = -7n + -1 + -1n Reorder the terms: -3(-7 + n) + 6(4 + 3n) = -7n + -1 + -1n (-7 * -3 + n * -3) + 6(4 + 3n) = -7n + -1 + -1n (21 + -3n) + 6(4 + 3n) = -7n + -1 + -1n 21 + -3n + (4 * 6 + 3n * 6) = -7n + -1 + -1n 21 + -3n + (24 + 18n) = -7n + -1 + -1n Reorder the terms: 21 + 24 + -3n + 18n = -7n + -1 + -1n Combine like terms: 21 + 24 = 45 45 + -3n + 18n = -7n + -1 + -1n Combine like terms: -3n + 18n = 15n 45 + 15n = -7n + -1 + -1n Reorder the terms: 45 + 15n = -1 + -7n + -1n Combine like terms: -7n + -1n = -8n 45 + 15n = -1 + -8n Solving 45 + 15n = -1 + -8n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8n' to each side of the equation. 45 + 15n + 8n = -1 + -8n + 8n Combine like terms: 15n + 8n = 23n 45 + 23n = -1 + -8n + 8n Combine like terms: -8n + 8n = 0 45 + 23n = -1 + 0 45 + 23n = -1 Add '-45' to each side of the equation. 45 + -45 + 23n = -1 + -45 Combine like terms: 45 + -45 = 0 0 + 23n = -1 + -45 23n = -1 + -45 Combine like terms: -1 + -45 = -46 23n = -46 Divide each side by '23'. n = -2 Simplifying n = -2
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