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Simplifying 7(1 + 7n) = 7(1 + -8n) (1 * 7 + 7n * 7) = 7(1 + -8n) (7 + 49n) = 7(1 + -8n) 7 + 49n = (1 * 7 + -8n * 7) 7 + 49n = (7 + -56n) Add '-7' to each side of the equation. 7 + -7 + 49n = 7 + -7 + -56n Combine like terms: 7 + -7 = 0 0 + 49n = 7 + -7 + -56n 49n = 7 + -7 + -56n Combine like terms: 7 + -7 = 0 49n = 0 + -56n 49n = -56n Solving 49n = -56n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '56n' to each side of the equation. 49n + 56n = -56n + 56n Combine like terms: 49n + 56n = 105n 105n = -56n + 56n Combine like terms: -56n + 56n = 0 105n = 0 Divide each side by '105'. n = 0 Simplifying n = 0
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