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Simplifying 5(m + -2n) + -1(2m + -1n) = 0 (m * 5 + -2n * 5) + -1(2m + -1n) = 0 (5m + -10n) + -1(2m + -1n) = 0 5m + -10n + (2m * -1 + -1n * -1) = 0 5m + -10n + (-2m + 1n) = 0 Reorder the terms: 5m + -2m + -10n + 1n = 0 Combine like terms: 5m + -2m = 3m 3m + -10n + 1n = 0 Combine like terms: -10n + 1n = -9n 3m + -9n = 0 Solving 3m + -9n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9n' to each side of the equation. 3m + -9n + 9n = 0 + 9n Combine like terms: -9n + 9n = 0 3m + 0 = 0 + 9n 3m = 0 + 9n Remove the zero: 3m = 9n Divide each side by '3'. m = 3n Simplifying m = 3n
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