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Simplifying -54 = 5(6 + -7n) + -1(8 + 3n) -54 = (6 * 5 + -7n * 5) + -1(8 + 3n) -54 = (30 + -35n) + -1(8 + 3n) -54 = 30 + -35n + (8 * -1 + 3n * -1) -54 = 30 + -35n + (-8 + -3n) Reorder the terms: -54 = 30 + -8 + -35n + -3n Combine like terms: 30 + -8 = 22 -54 = 22 + -35n + -3n Combine like terms: -35n + -3n = -38n -54 = 22 + -38n Solving -54 = 22 + -38n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '38n' to each side of the equation. -54 + 38n = 22 + -38n + 38n Combine like terms: -38n + 38n = 0 -54 + 38n = 22 + 0 -54 + 38n = 22 Add '54' to each side of the equation. -54 + 54 + 38n = 22 + 54 Combine like terms: -54 + 54 = 0 0 + 38n = 22 + 54 38n = 22 + 54 Combine like terms: 22 + 54 = 76 38n = 76 Divide each side by '38'. n = 2 Simplifying n = 2
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