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Simplifying 3(4n + -1) + 2(5 + -3n) = 7n Reorder the terms: 3(-1 + 4n) + 2(5 + -3n) = 7n (-1 * 3 + 4n * 3) + 2(5 + -3n) = 7n (-3 + 12n) + 2(5 + -3n) = 7n -3 + 12n + (5 * 2 + -3n * 2) = 7n -3 + 12n + (10 + -6n) = 7n Reorder the terms: -3 + 10 + 12n + -6n = 7n Combine like terms: -3 + 10 = 7 7 + 12n + -6n = 7n Combine like terms: 12n + -6n = 6n 7 + 6n = 7n Solving 7 + 6n = 7n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7n' to each side of the equation. 7 + 6n + -7n = 7n + -7n Combine like terms: 6n + -7n = -1n 7 + -1n = 7n + -7n Combine like terms: 7n + -7n = 0 7 + -1n = 0 Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7
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