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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 = -4 -4 + 8n + -3n = 6(n + -7) + 8 Combine like terms: 8n + -3n = 5n -4 + 5n = 6(n + -7) + 8 Reorder the terms: -4 + 5n = 6(-7 + n) + 8 -4 + 5n = (-7 * 6 + n * 6) + 8 -4 + 5n = (-42 + 6n) + 8 Reorder the terms: -4 + 5n = -42 + 8 + 6n Combine like terms: -42 + 8 = -34 -4 + 5n = -34 + 6n Solving -4 + 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. -4 + 5n + -6n = -34 + 6n + -6n Combine like terms: 5n + -6n = -1n -4 + -1n = -34 + 6n + -6n Combine like terms: 6n + -6n = 0 -4 + -1n = -34 + 0 -4 + -1n = -34 Add '4' to each side of the equation. -4 + 4 + -1n = -34 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = -34 + 4 -1n = -34 + 4 Combine like terms: -34 + 4 = -30 -1n = -30 Divide each side by '-1'. n = 30 Simplifying n = 30
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