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Simplifying 3(4n + -1) = 4(n + 9) + -7 Reorder the terms: 3(-1 + 4n) = 4(n + 9) + -7 (-1 * 3 + 4n * 3) = 4(n + 9) + -7 (-3 + 12n) = 4(n + 9) + -7 Reorder the terms: -3 + 12n = 4(9 + n) + -7 -3 + 12n = (9 * 4 + n * 4) + -7 -3 + 12n = (36 + 4n) + -7 Reorder the terms: -3 + 12n = 36 + -7 + 4n Combine like terms: 36 + -7 = 29 -3 + 12n = 29 + 4n Solving -3 + 12n = 29 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. -3 + 12n + -4n = 29 + 4n + -4n Combine like terms: 12n + -4n = 8n -3 + 8n = 29 + 4n + -4n Combine like terms: 4n + -4n = 0 -3 + 8n = 29 + 0 -3 + 8n = 29 Add '3' to each side of the equation. -3 + 3 + 8n = 29 + 3 Combine like terms: -3 + 3 = 0 0 + 8n = 29 + 3 8n = 29 + 3 Combine like terms: 29 + 3 = 32 8n = 32 Divide each side by '8'. n = 4 Simplifying n = 4
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