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Simplifying 34n + 4(30 + -3n) = 24(n + 6) 34n + (30 * 4 + -3n * 4) = 24(n + 6) 34n + (120 + -12n) = 24(n + 6) Reorder the terms: 120 + 34n + -12n = 24(n + 6) Combine like terms: 34n + -12n = 22n 120 + 22n = 24(n + 6) Reorder the terms: 120 + 22n = 24(6 + n) 120 + 22n = (6 * 24 + n * 24) 120 + 22n = (144 + 24n) Solving 120 + 22n = 144 + 24n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24n' to each side of the equation. 120 + 22n + -24n = 144 + 24n + -24n Combine like terms: 22n + -24n = -2n 120 + -2n = 144 + 24n + -24n Combine like terms: 24n + -24n = 0 120 + -2n = 144 + 0 120 + -2n = 144 Add '-120' to each side of the equation. 120 + -120 + -2n = 144 + -120 Combine like terms: 120 + -120 = 0 0 + -2n = 144 + -120 -2n = 144 + -120 Combine like terms: 144 + -120 = 24 -2n = 24 Divide each side by '-2'. n = -12 Simplifying n = -12
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