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Simplifying 5(3n + 34) + 8(n + 1) = 0 Reorder the terms: 5(34 + 3n) + 8(n + 1) = 0 (34 * 5 + 3n * 5) + 8(n + 1) = 0 (170 + 15n) + 8(n + 1) = 0 Reorder the terms: 170 + 15n + 8(1 + n) = 0 170 + 15n + (1 * 8 + n * 8) = 0 170 + 15n + (8 + 8n) = 0 Reorder the terms: 170 + 8 + 15n + 8n = 0 Combine like terms: 170 + 8 = 178 178 + 15n + 8n = 0 Combine like terms: 15n + 8n = 23n 178 + 23n = 0 Solving 178 + 23n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-178' to each side of the equation. 178 + -178 + 23n = 0 + -178 Combine like terms: 178 + -178 = 0 0 + 23n = 0 + -178 23n = 0 + -178 Combine like terms: 0 + -178 = -178 23n = -178 Divide each side by '23'. n = -7.739130435 Simplifying n = -7.739130435
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