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Simplifying 7 + 5 = 12(8M + 7N) + 13(5M + 9N) + 15(12M + 17N) Combine like terms: 7 + 5 = 12 12 = 12(8M + 7N) + 13(5M + 9N) + 15(12M + 17N) 12 = (8M * 12 + 7N * 12) + 13(5M + 9N) + 15(12M + 17N) 12 = (96M + 84N) + 13(5M + 9N) + 15(12M + 17N) 12 = 96M + 84N + (5M * 13 + 9N * 13) + 15(12M + 17N) 12 = 96M + 84N + (65M + 117N) + 15(12M + 17N) 12 = 96M + 84N + 65M + 117N + (12M * 15 + 17N * 15) 12 = 96M + 84N + 65M + 117N + (180M + 255N) Reorder the terms: 12 = 96M + 65M + 180M + 84N + 117N + 255N Combine like terms: 96M + 65M = 161M 12 = 161M + 180M + 84N + 117N + 255N Combine like terms: 161M + 180M = 341M 12 = 341M + 84N + 117N + 255N Combine like terms: 84N + 117N = 201N 12 = 341M + 201N + 255N Combine like terms: 201N + 255N = 456N 12 = 341M + 456N Solving 12 = 341M + 456N Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-341M' to each side of the equation. 12 + -341M = 341M + -341M + 456N Combine like terms: 341M + -341M = 0 12 + -341M = 0 + 456N 12 + -341M = 456N Add '-12' to each side of the equation. 12 + -12 + -341M = -12 + 456N Combine like terms: 12 + -12 = 0 0 + -341M = -12 + 456N -341M = -12 + 456N Divide each side by '-341'. M = 0.03519061584 + -1.337243402N Simplifying M = 0.03519061584 + -1.337243402N
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