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Simplifying 5(2m + 3) + -1(1 + -2m) = 2[3(3 + 2m) + -1(3 + -1m)] Reorder the terms: 5(3 + 2m) + -1(1 + -2m) = 2[3(3 + 2m) + -1(3 + -1m)] (3 * 5 + 2m * 5) + -1(1 + -2m) = 2[3(3 + 2m) + -1(3 + -1m)] (15 + 10m) + -1(1 + -2m) = 2[3(3 + 2m) + -1(3 + -1m)] 15 + 10m + (1 * -1 + -2m * -1) = 2[3(3 + 2m) + -1(3 + -1m)] 15 + 10m + (-1 + 2m) = 2[3(3 + 2m) + -1(3 + -1m)] Reorder the terms: 15 + -1 + 10m + 2m = 2[3(3 + 2m) + -1(3 + -1m)] Combine like terms: 15 + -1 = 14 14 + 10m + 2m = 2[3(3 + 2m) + -1(3 + -1m)] Combine like terms: 10m + 2m = 12m 14 + 12m = 2[3(3 + 2m) + -1(3 + -1m)] 14 + 12m = 2[(3 * 3 + 2m * 3) + -1(3 + -1m)] 14 + 12m = 2[(9 + 6m) + -1(3 + -1m)] 14 + 12m = 2[9 + 6m + (3 * -1 + -1m * -1)] 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 = 7m 14 + 12m = 2[6 + 7m] 14 + 12m = [6 * 2 + 7m * 2] 14 + 12m = [12 + 14m] Solving 14 + 12m = 12 + 14m Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-14m' to each side of the equation. 14 + 12m + -14m = 12 + 14m + -14m Combine like terms: 12m + -14m = -2m 14 + -2m = 12 + 14m + -14m Combine like terms: 14m + -14m = 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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