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Simplifying 0.05(0.3m + 35n) + -0.8(-0.09n + -22M) = 0 (0.3m * 0.05 + 35n * 0.05) + -0.8(-0.09n + -22M) = 0 (0.015m + 1.75n) + -0.8(-0.09n + -22M) = 0 Reorder the terms: 0.015m + 1.75n + -0.8(-22M + -0.09n) = 0 0.015m + 1.75n + (-22M * -0.8 + -0.09n * -0.8) = 0 0.015m + 1.75n + (17.6M + 0.072n) = 0 Reorder the terms: 17.6M + 0.015m + 1.75n + 0.072n = 0 Combine like terms: 1.75n + 0.072n = 1.822n 17.6M + 0.015m + 1.822n = 0 Solving 17.6M + 0.015m + 1.822n = 0 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-0.015m' to each side of the equation. 17.6M + 0.015m + -0.015m + 1.822n = 0 + -0.015m Combine like terms: 0.015m + -0.015m = 0.000 17.6M + 0.000 + 1.822n = 0 + -0.015m 17.6M + 1.822n = 0 + -0.015m Remove the zero: 17.6M + 1.822n = -0.015m Add '-1.822n' to each side of the equation. 17.6M + 1.822n + -1.822n = -0.015m + -1.822n Combine like terms: 1.822n + -1.822n = 0.000 17.6M + 0.000 = -0.015m + -1.822n 17.6M = -0.015m + -1.822n Divide each side by '17.6'. M = -0.0008522727273m + -0.1035227273n Simplifying M = -0.0008522727273m + -0.1035227273n
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