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Simplifying 3(m + n) + 4(2m + -3) + 2(5 + -1n) = 0 (m * 3 + n * 3) + 4(2m + -3) + 2(5 + -1n) = 0 (3m + 3n) + 4(2m + -3) + 2(5 + -1n) = 0 Reorder the terms: 3m + 3n + 4(-3 + 2m) + 2(5 + -1n) = 0 3m + 3n + (-3 * 4 + 2m * 4) + 2(5 + -1n) = 0 3m + 3n + (-12 + 8m) + 2(5 + -1n) = 0 3m + 3n + -12 + 8m + (5 * 2 + -1n * 2) = 0 3m + 3n + -12 + 8m + (10 + -2n) = 0 Reorder the terms: -12 + 10 + 3m + 8m + 3n + -2n = 0 Combine like terms: -12 + 10 = -2 -2 + 3m + 8m + 3n + -2n = 0 Combine like terms: 3m + 8m = 11m -2 + 11m + 3n + -2n = 0 Combine like terms: 3n + -2n = 1n -2 + 11m + 1n = 0 Solving -2 + 11m + 1n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 11m + 2 + 1n = 0 + 2 Reorder the terms: -2 + 2 + 11m + 1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 11m + 1n = 0 + 2 11m + 1n = 0 + 2 Combine like terms: 0 + 2 = 2 11m + 1n = 2 Add '-1n' to each side of the equation. 11m + 1n + -1n = 2 + -1n Combine like terms: 1n + -1n = 0 11m + 0 = 2 + -1n 11m = 2 + -1n Divide each side by '11'. m = 0.1818181818 + -0.09090909091n Simplifying m = 0.1818181818 + -0.09090909091n
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