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Simplifying 54 = 6(n + -1) + 7(n + 3) Reorder the terms: 54 = 6(-1 + n) + 7(n + 3) 54 = (-1 * 6 + n * 6) + 7(n + 3) 54 = (-6 + 6n) + 7(n + 3) Reorder the terms: 54 = -6 + 6n + 7(3 + n) 54 = -6 + 6n + (3 * 7 + n * 7) 54 = -6 + 6n + (21 + 7n) Reorder the terms: 54 = -6 + 21 + 6n + 7n Combine like terms: -6 + 21 = 15 54 = 15 + 6n + 7n Combine like terms: 6n + 7n = 13n 54 = 15 + 13n Solving 54 = 15 + 13n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-13n' to each side of the equation. 54 + -13n = 15 + 13n + -13n Combine like terms: 13n + -13n = 0 54 + -13n = 15 + 0 54 + -13n = 15 Add '-54' to each side of the equation. 54 + -54 + -13n = 15 + -54 Combine like terms: 54 + -54 = 0 0 + -13n = 15 + -54 -13n = 15 + -54 Combine like terms: 15 + -54 = -39 -13n = -39 Divide each side by '-13'. n = 3 Simplifying n = 3
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