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Simplifying 5n + -1(7n + 3) = 7 + -1(10n + -9) Reorder the terms: 5n + -1(3 + 7n) = 7 + -1(10n + -9) 5n + (3 * -1 + 7n * -1) = 7 + -1(10n + -9) 5n + (-3 + -7n) = 7 + -1(10n + -9) Reorder the terms: -3 + 5n + -7n = 7 + -1(10n + -9) Combine like terms: 5n + -7n = -2n -3 + -2n = 7 + -1(10n + -9) Reorder the terms: -3 + -2n = 7 + -1(-9 + 10n) -3 + -2n = 7 + (-9 * -1 + 10n * -1) -3 + -2n = 7 + (9 + -10n) Combine like terms: 7 + 9 = 16 -3 + -2n = 16 + -10n Solving -3 + -2n = 16 + -10n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '10n' to each side of the equation. -3 + -2n + 10n = 16 + -10n + 10n Combine like terms: -2n + 10n = 8n -3 + 8n = 16 + -10n + 10n Combine like terms: -10n + 10n = 0 -3 + 8n = 16 + 0 -3 + 8n = 16 Add '3' to each side of the equation. -3 + 3 + 8n = 16 + 3 Combine like terms: -3 + 3 = 0 0 + 8n = 16 + 3 8n = 16 + 3 Combine like terms: 16 + 3 = 19 8n = 19 Divide each side by '8'. n = 2.375 Simplifying n = 2.375
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