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Simplifying 5(9n + 31) + 7(n + 1) = 0 Reorder the terms: 5(31 + 9n) + 7(n + 1) = 0 (31 * 5 + 9n * 5) + 7(n + 1) = 0 (155 + 45n) + 7(n + 1) = 0 Reorder the terms: 155 + 45n + 7(1 + n) = 0 155 + 45n + (1 * 7 + n * 7) = 0 155 + 45n + (7 + 7n) = 0 Reorder the terms: 155 + 7 + 45n + 7n = 0 Combine like terms: 155 + 7 = 162 162 + 45n + 7n = 0 Combine like terms: 45n + 7n = 52n 162 + 52n = 0 Solving 162 + 52n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-162' to each side of the equation. 162 + -162 + 52n = 0 + -162 Combine like terms: 162 + -162 = 0 0 + 52n = 0 + -162 52n = 0 + -162 Combine like terms: 0 + -162 = -162 52n = -162 Divide each side by '52'. n = -3.115384615 Simplifying n = -3.115384615
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