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Simplifying 8(2n + 1) + -1(n + -9) = -52 + -8n Reorder the terms: 8(1 + 2n) + -1(n + -9) = -52 + -8n (1 * 8 + 2n * 8) + -1(n + -9) = -52 + -8n (8 + 16n) + -1(n + -9) = -52 + -8n Reorder the terms: 8 + 16n + -1(-9 + n) = -52 + -8n 8 + 16n + (-9 * -1 + n * -1) = -52 + -8n 8 + 16n + (9 + -1n) = -52 + -8n Reorder the terms: 8 + 9 + 16n + -1n = -52 + -8n Combine like terms: 8 + 9 = 17 17 + 16n + -1n = -52 + -8n Combine like terms: 16n + -1n = 15n 17 + 15n = -52 + -8n Solving 17 + 15n = -52 + -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. 17 + 15n + 8n = -52 + -8n + 8n Combine like terms: 15n + 8n = 23n 17 + 23n = -52 + -8n + 8n Combine like terms: -8n + 8n = 0 17 + 23n = -52 + 0 17 + 23n = -52 Add '-17' to each side of the equation. 17 + -17 + 23n = -52 + -17 Combine like terms: 17 + -17 = 0 0 + 23n = -52 + -17 23n = -52 + -17 Combine like terms: -52 + -17 = -69 23n = -69 Divide each side by '23'. n = -3 Simplifying n = -3
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