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Simplifying 7(2n + 1) = 8(4n + 9) + 8 Reorder the terms: 7(1 + 2n) = 8(4n + 9) + 8 (1 * 7 + 2n * 7) = 8(4n + 9) + 8 (7 + 14n) = 8(4n + 9) + 8 Reorder the terms: 7 + 14n = 8(9 + 4n) + 8 7 + 14n = (9 * 8 + 4n * 8) + 8 7 + 14n = (72 + 32n) + 8 Reorder the terms: 7 + 14n = 72 + 8 + 32n Combine like terms: 72 + 8 = 80 7 + 14n = 80 + 32n Solving 7 + 14n = 80 + 32n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-32n' to each side of the equation. 7 + 14n + -32n = 80 + 32n + -32n Combine like terms: 14n + -32n = -18n 7 + -18n = 80 + 32n + -32n Combine like terms: 32n + -32n = 0 7 + -18n = 80 + 0 7 + -18n = 80 Add '-7' to each side of the equation. 7 + -7 + -18n = 80 + -7 Combine like terms: 7 + -7 = 0 0 + -18n = 80 + -7 -18n = 80 + -7 Combine like terms: 80 + -7 = 73 -18n = 73 Divide each side by '-18'. n = -4.055555556 Simplifying n = -4.055555556
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