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Simplifying 5(2m + 3) + -1(1 + -2m) = 2[3(3 + 2m) + -3 + -1m] Reorder the terms: 5(3 + 2m) + -1(1 + -2m) = 2[3(3 + 2m) + -3 + -1m] (3 * 5 + 2m * 5) + -1(1 + -2m) = 2[3(3 + 2m) + -3 + -1m] (15 + 10m) + -1(1 + -2m) = 2[3(3 + 2m) + -3 + -1m] 15 + 10m + (1 * -1 + -2m * -1) = 2[3(3 + 2m) + -3 + -1m] 15 + 10m + (-1 + 2m) = 2[3(3 + 2m) + -3 + -1m] Reorder the terms: 15 + -1 + 10m + 2m = 2[3(3 + 2m) + -3 + -1m] Combine like terms: 15 + -1 = 14 14 + 10m + 2m = 2[3(3 + 2m) + -3 + -1m] Combine like terms: 10m + 2m = 12m 14 + 12m = 2[3(3 + 2m) + -3 + -1m] 14 + 12m = 2[(3 * 3 + 2m * 3) + -3 + -1m] 14 + 12m = 2[(9 + 6m) + -3 + -1m] Reorder the terms: 14 + 12m = 2[9 + -3 + 6m + -1m] Combine like terms: 9 + -3 = 6 14 + 12m = 2[6 + 6m + -1m] Combine like terms: 6m + -1m = 5m 14 + 12m = 2[6 + 5m] 14 + 12m = [6 * 2 + 5m * 2] 14 + 12m = [12 + 10m] Solving 14 + 12m = 12 + 10m Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-10m' to each side of the equation. 14 + 12m + -10m = 12 + 10m + -10m Combine like terms: 12m + -10m = 2m 14 + 2m = 12 + 10m + -10m Combine like terms: 10m + -10m = 0 14 + 2m = 12 + 0 14 + 2m = 12 Add '-14' to each side of the equation. 14 + -14 + 2m = 12 + -14 Combine like terms: 14 + -14 = 0 0 + 2m = 12 + -14 2m = 12 + -14 Combine like terms: 12 + -14 = -2 2m = -2 Divide each side by '2'. m = -1 Simplifying m = -1
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