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Simplifying 8(n + 1) + 3(-4n + -3) = 7 + -7n + 2n + 7 Reorder the terms: 8(1 + n) + 3(-4n + -3) = 7 + -7n + 2n + 7 (1 * 8 + n * 8) + 3(-4n + -3) = 7 + -7n + 2n + 7 (8 + 8n) + 3(-4n + -3) = 7 + -7n + 2n + 7 Reorder the terms: 8 + 8n + 3(-3 + -4n) = 7 + -7n + 2n + 7 8 + 8n + (-3 * 3 + -4n * 3) = 7 + -7n + 2n + 7 8 + 8n + (-9 + -12n) = 7 + -7n + 2n + 7 Reorder the terms: 8 + -9 + 8n + -12n = 7 + -7n + 2n + 7 Combine like terms: 8 + -9 = -1 -1 + 8n + -12n = 7 + -7n + 2n + 7 Combine like terms: 8n + -12n = -4n -1 + -4n = 7 + -7n + 2n + 7 Reorder the terms: -1 + -4n = 7 + 7 + -7n + 2n Combine like terms: 7 + 7 = 14 -1 + -4n = 14 + -7n + 2n Combine like terms: -7n + 2n = -5n -1 + -4n = 14 + -5n Solving -1 + -4n = 14 + -5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5n' to each side of the equation. -1 + -4n + 5n = 14 + -5n + 5n Combine like terms: -4n + 5n = 1n -1 + 1n = 14 + -5n + 5n Combine like terms: -5n + 5n = 0 -1 + 1n = 14 + 0 -1 + 1n = 14 Add '1' to each side of the equation. -1 + 1 + 1n = 14 + 1 Combine like terms: -1 + 1 = 0 0 + 1n = 14 + 1 1n = 14 + 1 Combine like terms: 14 + 1 = 15 1n = 15 Divide each side by '1'. n = 15 Simplifying n = 15
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