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Simplifying n + 8n = 8(n + -4) + 4(n + -9) Combine like terms: n + 8n = 9n 9n = 8(n + -4) + 4(n + -9) Reorder the terms: 9n = 8(-4 + n) + 4(n + -9) 9n = (-4 * 8 + n * 8) + 4(n + -9) 9n = (-32 + 8n) + 4(n + -9) Reorder the terms: 9n = -32 + 8n + 4(-9 + n) 9n = -32 + 8n + (-9 * 4 + n * 4) 9n = -32 + 8n + (-36 + 4n) Reorder the terms: 9n = -32 + -36 + 8n + 4n Combine like terms: -32 + -36 = -68 9n = -68 + 8n + 4n Combine like terms: 8n + 4n = 12n 9n = -68 + 12n Solving 9n = -68 + 12n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-12n' to each side of the equation. 9n + -12n = -68 + 12n + -12n Combine like terms: 9n + -12n = -3n -3n = -68 + 12n + -12n Combine like terms: 12n + -12n = 0 -3n = -68 + 0 -3n = -68 Divide each side by '-3'. n = 22.66666667 Simplifying n = 22.66666667
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