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Simplifying 0.5(0.3m + 35n) + -0.8(-0.09n + -22m) = 0 (0.3m * 0.5 + 35n * 0.5) + -0.8(-0.09n + -22m) = 0 (0.15m + 17.5n) + -0.8(-0.09n + -22m) = 0 Reorder the terms: 0.15m + 17.5n + -0.8(-22m + -0.09n) = 0 0.15m + 17.5n + (-22m * -0.8 + -0.09n * -0.8) = 0 0.15m + 17.5n + (17.6m + 0.072n) = 0 Reorder the terms: 0.15m + 17.6m + 17.5n + 0.072n = 0 Combine like terms: 0.15m + 17.6m = 17.75m 17.75m + 17.5n + 0.072n = 0 Combine like terms: 17.5n + 0.072n = 17.572n 17.75m + 17.572n = 0 Solving 17.75m + 17.572n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-17.572n' to each side of the equation. 17.75m + 17.572n + -17.572n = 0 + -17.572n Combine like terms: 17.572n + -17.572n = 0.000 17.75m + 0.000 = 0 + -17.572n 17.75m = 0 + -17.572n Remove the zero: 17.75m = -17.572n Divide each side by '17.75'. m = -0.989971831n Simplifying m = -0.989971831n
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