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Simplifying 4(2n + 34) + 7(n + 1) = 0 Reorder the terms: 4(34 + 2n) + 7(n + 1) = 0 (34 * 4 + 2n * 4) + 7(n + 1) = 0 (136 + 8n) + 7(n + 1) = 0 Reorder the terms: 136 + 8n + 7(1 + n) = 0 136 + 8n + (1 * 7 + n * 7) = 0 136 + 8n + (7 + 7n) = 0 Reorder the terms: 136 + 7 + 8n + 7n = 0 Combine like terms: 136 + 7 = 143 143 + 8n + 7n = 0 Combine like terms: 8n + 7n = 15n 143 + 15n = 0 Solving 143 + 15n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-143' to each side of the equation. 143 + -143 + 15n = 0 + -143 Combine like terms: 143 + -143 = 0 0 + 15n = 0 + -143 15n = 0 + -143 Combine like terms: 0 + -143 = -143 15n = -143 Divide each side by '15'. n = -9.533333333 Simplifying n = -9.533333333
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