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Simplifying -4n + 7n = 3(1 + -4n) + 6(-4 + 3n) Combine like terms: -4n + 7n = 3n 3n = 3(1 + -4n) + 6(-4 + 3n) 3n = (1 * 3 + -4n * 3) + 6(-4 + 3n) 3n = (3 + -12n) + 6(-4 + 3n) 3n = 3 + -12n + (-4 * 6 + 3n * 6) 3n = 3 + -12n + (-24 + 18n) Reorder the terms: 3n = 3 + -24 + -12n + 18n Combine like terms: 3 + -24 = -21 3n = -21 + -12n + 18n Combine like terms: -12n + 18n = 6n 3n = -21 + 6n Solving 3n = -21 + 6n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6n' to each side of the equation. 3n + -6n = -21 + 6n + -6n Combine like terms: 3n + -6n = -3n -3n = -21 + 6n + -6n Combine like terms: 6n + -6n = 0 -3n = -21 + 0 -3n = -21 Divide each side by '-3'. n = 7 Simplifying n = 7
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