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Simplifying -42 = -6(-4n + 3) + 7(n + 1) Reorder the terms: -42 = -6(3 + -4n) + 7(n + 1) -42 = (3 * -6 + -4n * -6) + 7(n + 1) -42 = (-18 + 24n) + 7(n + 1) Reorder the terms: -42 = -18 + 24n + 7(1 + n) -42 = -18 + 24n + (1 * 7 + n * 7) -42 = -18 + 24n + (7 + 7n) Reorder the terms: -42 = -18 + 7 + 24n + 7n Combine like terms: -18 + 7 = -11 -42 = -11 + 24n + 7n Combine like terms: 24n + 7n = 31n -42 = -11 + 31n Solving -42 = -11 + 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. -42 + -31n = -11 + 31n + -31n Combine like terms: 31n + -31n = 0 -42 + -31n = -11 + 0 -42 + -31n = -11 Add '42' to each side of the equation. -42 + 42 + -31n = -11 + 42 Combine like terms: -42 + 42 = 0 0 + -31n = -11 + 42 -31n = -11 + 42 Combine like terms: -11 + 42 = 31 -31n = 31 Divide each side by '-31'. n = -1 Simplifying n = -1
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