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Simplifying -6(10 + -7n) + -3(5 + 9n) = n + -10 + 9n + 5 (10 * -6 + -7n * -6) + -3(5 + 9n) = n + -10 + 9n + 5 (-60 + 42n) + -3(5 + 9n) = n + -10 + 9n + 5 -60 + 42n + (5 * -3 + 9n * -3) = n + -10 + 9n + 5 -60 + 42n + (-15 + -27n) = n + -10 + 9n + 5 Reorder the terms: -60 + -15 + 42n + -27n = n + -10 + 9n + 5 Combine like terms: -60 + -15 = -75 -75 + 42n + -27n = n + -10 + 9n + 5 Combine like terms: 42n + -27n = 15n -75 + 15n = n + -10 + 9n + 5 Reorder the terms: -75 + 15n = -10 + 5 + n + 9n Combine like terms: -10 + 5 = -5 -75 + 15n = -5 + n + 9n Combine like terms: n + 9n = 10n -75 + 15n = -5 + 10n Solving -75 + 15n = -5 + 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. -75 + 15n + -10n = -5 + 10n + -10n Combine like terms: 15n + -10n = 5n -75 + 5n = -5 + 10n + -10n Combine like terms: 10n + -10n = 0 -75 + 5n = -5 + 0 -75 + 5n = -5 Add '75' to each side of the equation. -75 + 75 + 5n = -5 + 75 Combine like terms: -75 + 75 = 0 0 + 5n = -5 + 75 5n = -5 + 75 Combine like terms: -5 + 75 = 70 5n = 70 Divide each side by '5'. n = 14 Simplifying n = 14
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