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Simplifying 11 + -8n + 12n + -7 = 9(5n + 7) + -9(5n + 3) Reorder the terms: 11 + -7 + -8n + 12n = 9(5n + 7) + -9(5n + 3) Combine like terms: 11 + -7 = 4 4 + -8n + 12n = 9(5n + 7) + -9(5n + 3) Combine like terms: -8n + 12n = 4n 4 + 4n = 9(5n + 7) + -9(5n + 3) Reorder the terms: 4 + 4n = 9(7 + 5n) + -9(5n + 3) 4 + 4n = (7 * 9 + 5n * 9) + -9(5n + 3) 4 + 4n = (63 + 45n) + -9(5n + 3) Reorder the terms: 4 + 4n = 63 + 45n + -9(3 + 5n) 4 + 4n = 63 + 45n + (3 * -9 + 5n * -9) 4 + 4n = 63 + 45n + (-27 + -45n) Reorder the terms: 4 + 4n = 63 + -27 + 45n + -45n Combine like terms: 63 + -27 = 36 4 + 4n = 36 + 45n + -45n Combine like terms: 45n + -45n = 0 4 + 4n = 36 + 0 4 + 4n = 36 Solving 4 + 4n = 36 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 4n = 36 + -4 Combine like terms: 4 + -4 = 0 0 + 4n = 36 + -4 4n = 36 + -4 Combine like terms: 36 + -4 = 32 4n = 32 Divide each side by '4'. n = 8 Simplifying n = 8
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