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Simplifying 4(n + 9) + n = 66 + -1(n + -12) Reorder the terms: 4(9 + n) + n = 66 + -1(n + -12) (9 * 4 + n * 4) + n = 66 + -1(n + -12) (36 + 4n) + n = 66 + -1(n + -12) Combine like terms: 4n + n = 5n 36 + 5n = 66 + -1(n + -12) Reorder the terms: 36 + 5n = 66 + -1(-12 + n) 36 + 5n = 66 + (-12 * -1 + n * -1) 36 + 5n = 66 + (12 + -1n) Combine like terms: 66 + 12 = 78 36 + 5n = 78 + -1n Solving 36 + 5n = 78 + -1n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add 'n' to each side of the equation. 36 + 5n + n = 78 + -1n + n Combine like terms: 5n + n = 6n 36 + 6n = 78 + -1n + n Combine like terms: -1n + n = 0 36 + 6n = 78 + 0 36 + 6n = 78 Add '-36' to each side of the equation. 36 + -36 + 6n = 78 + -36 Combine like terms: 36 + -36 = 0 0 + 6n = 78 + -36 6n = 78 + -36 Combine like terms: 78 + -36 = 42 6n = 42 Divide each side by '6'. n = 7 Simplifying n = 7
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