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Simplifying 12(4 + n) + 5(-2n + -9) = -19 (4 * 12 + n * 12) + 5(-2n + -9) = -19 (48 + 12n) + 5(-2n + -9) = -19 Reorder the terms: 48 + 12n + 5(-9 + -2n) = -19 48 + 12n + (-9 * 5 + -2n * 5) = -19 48 + 12n + (-45 + -10n) = -19 Reorder the terms: 48 + -45 + 12n + -10n = -19 Combine like terms: 48 + -45 = 3 3 + 12n + -10n = -19 Combine like terms: 12n + -10n = 2n 3 + 2n = -19 Solving 3 + 2n = -19 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2n = -19 + -3 Combine like terms: 3 + -3 = 0 0 + 2n = -19 + -3 2n = -19 + -3 Combine like terms: -19 + -3 = -22 2n = -22 Divide each side by '2'. n = -11 Simplifying n = -11
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