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Simplifying -7(12 + 7n) = -7n + 6(1 + -4n) (12 * -7 + 7n * -7) = -7n + 6(1 + -4n) (-84 + -49n) = -7n + 6(1 + -4n) -84 + -49n = -7n + (1 * 6 + -4n * 6) -84 + -49n = -7n + (6 + -24n) Reorder the terms: -84 + -49n = 6 + -7n + -24n Combine like terms: -7n + -24n = -31n -84 + -49n = 6 + -31n Solving -84 + -49n = 6 + -31n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '31n' to each side of the equation. -84 + -49n + 31n = 6 + -31n + 31n Combine like terms: -49n + 31n = -18n -84 + -18n = 6 + -31n + 31n Combine like terms: -31n + 31n = 0 -84 + -18n = 6 + 0 -84 + -18n = 6 Add '84' to each side of the equation. -84 + 84 + -18n = 6 + 84 Combine like terms: -84 + 84 = 0 0 + -18n = 6 + 84 -18n = 6 + 84 Combine like terms: 6 + 84 = 90 -18n = 90 Divide each side by '-18'. n = -5 Simplifying n = -5
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