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Simplifying 4(2n + 1) = 6(4n + 7) + 1 Reorder the terms: 4(1 + 2n) = 6(4n + 7) + 1 (1 * 4 + 2n * 4) = 6(4n + 7) + 1 (4 + 8n) = 6(4n + 7) + 1 Reorder the terms: 4 + 8n = 6(7 + 4n) + 1 4 + 8n = (7 * 6 + 4n * 6) + 1 4 + 8n = (42 + 24n) + 1 Reorder the terms: 4 + 8n = 42 + 1 + 24n Combine like terms: 42 + 1 = 43 4 + 8n = 43 + 24n Solving 4 + 8n = 43 + 24n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24n' to each side of the equation. 4 + 8n + -24n = 43 + 24n + -24n Combine like terms: 8n + -24n = -16n 4 + -16n = 43 + 24n + -24n Combine like terms: 24n + -24n = 0 4 + -16n = 43 + 0 4 + -16n = 43 Add '-4' to each side of the equation. 4 + -4 + -16n = 43 + -4 Combine like terms: 4 + -4 = 0 0 + -16n = 43 + -4 -16n = 43 + -4 Combine like terms: 43 + -4 = 39 -16n = 39 Divide each side by '-16'. n = -2.4375 Simplifying n = -2.4375
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