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Simplifying 8(n + 2) + -3(n + -4) = 6(n + -7) + 8 Reorder the terms: 8(2 + n) + -3(n + -4) = 6(n + -7) + 8 (2 * 8 + n * 8) + -3(n + -4) = 6(n + -7) + 8 (16 + 8n) + -3(n + -4) = 6(n + -7) + 8 Reorder the terms: 16 + 8n + -3(-4 + n) = 6(n + -7) + 8 16 + 8n + (-4 * -3 + n * -3) = 6(n + -7) + 8 16 + 8n + (12 + -3n) = 6(n + -7) + 8 Reorder the terms: 16 + 12 + 8n + -3n = 6(n + -7) + 8 Combine like terms: 16 + 12 = 28 28 + 8n + -3n = 6(n + -7) + 8 Combine like terms: 8n + -3n = 5n 28 + 5n = 6(n + -7) + 8 Reorder the terms: 28 + 5n = 6(-7 + n) + 8 28 + 5n = (-7 * 6 + n * 6) + 8 28 + 5n = (-42 + 6n) + 8 Reorder the terms: 28 + 5n = -42 + 8 + 6n Combine like terms: -42 + 8 = -34 28 + 5n = -34 + 6n Solving 28 + 5n = -34 + 6n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6n' to each side of the equation. 28 + 5n + -6n = -34 + 6n + -6n Combine like terms: 5n + -6n = -1n 28 + -1n = -34 + 6n + -6n Combine like terms: 6n + -6n = 0 28 + -1n = -34 + 0 28 + -1n = -34 Add '-28' to each side of the equation. 28 + -28 + -1n = -34 + -28 Combine like terms: 28 + -28 = 0 0 + -1n = -34 + -28 -1n = -34 + -28 Combine like terms: -34 + -28 = -62 -1n = -62 Divide each side by '-1'. n = 62 Simplifying n = 62
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