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Simplifying (n + -1) + 4(n + -1) + 8(n + -1) = 78 Reorder the terms: (-1 + n) + 4(n + -1) + 8(n + -1) = 78 Remove parenthesis around (-1 + n) -1 + n + 4(n + -1) + 8(n + -1) = 78 Reorder the terms: -1 + n + 4(-1 + n) + 8(n + -1) = 78 -1 + n + (-1 * 4 + n * 4) + 8(n + -1) = 78 -1 + n + (-4 + 4n) + 8(n + -1) = 78 Reorder the terms: -1 + n + -4 + 4n + 8(-1 + n) = 78 -1 + n + -4 + 4n + (-1 * 8 + n * 8) = 78 -1 + n + -4 + 4n + (-8 + 8n) = 78 Reorder the terms: -1 + -4 + -8 + n + 4n + 8n = 78 Combine like terms: -1 + -4 = -5 -5 + -8 + n + 4n + 8n = 78 Combine like terms: -5 + -8 = -13 -13 + n + 4n + 8n = 78 Combine like terms: n + 4n = 5n -13 + 5n + 8n = 78 Combine like terms: 5n + 8n = 13n -13 + 13n = 78 Solving -13 + 13n = 78 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 13n = 78 + 13 Combine like terms: -13 + 13 = 0 0 + 13n = 78 + 13 13n = 78 + 13 Combine like terms: 78 + 13 = 91 13n = 91 Divide each side by '13'. n = 7 Simplifying n = 7
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