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Simplifying n + 3 + 2n = 3(-6n + -4) + 6(4n + -3) Reorder the terms: 3 + n + 2n = 3(-6n + -4) + 6(4n + -3) Combine like terms: n + 2n = 3n 3 + 3n = 3(-6n + -4) + 6(4n + -3) Reorder the terms: 3 + 3n = 3(-4 + -6n) + 6(4n + -3) 3 + 3n = (-4 * 3 + -6n * 3) + 6(4n + -3) 3 + 3n = (-12 + -18n) + 6(4n + -3) Reorder the terms: 3 + 3n = -12 + -18n + 6(-3 + 4n) 3 + 3n = -12 + -18n + (-3 * 6 + 4n * 6) 3 + 3n = -12 + -18n + (-18 + 24n) Reorder the terms: 3 + 3n = -12 + -18 + -18n + 24n Combine like terms: -12 + -18 = -30 3 + 3n = -30 + -18n + 24n Combine like terms: -18n + 24n = 6n 3 + 3n = -30 + 6n Solving 3 + 3n = -30 + 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. 3 + 3n + -6n = -30 + 6n + -6n Combine like terms: 3n + -6n = -3n 3 + -3n = -30 + 6n + -6n Combine like terms: 6n + -6n = 0 3 + -3n = -30 + 0 3 + -3n = -30 Add '-3' to each side of the equation. 3 + -3 + -3n = -30 + -3 Combine like terms: 3 + -3 = 0 0 + -3n = -30 + -3 -3n = -30 + -3 Combine like terms: -30 + -3 = -33 -3n = -33 Divide each side by '-3'. n = 11 Simplifying n = 11
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