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Simplifying 19d + -7(8d + 12) = 19 + -20d + -1 Reorder the terms: 19d + -7(12 + 8d) = 19 + -20d + -1 19d + (12 * -7 + 8d * -7) = 19 + -20d + -1 19d + (-84 + -56d) = 19 + -20d + -1 Reorder the terms: -84 + 19d + -56d = 19 + -20d + -1 Combine like terms: 19d + -56d = -37d -84 + -37d = 19 + -20d + -1 Reorder the terms: -84 + -37d = 19 + -1 + -20d Combine like terms: 19 + -1 = 18 -84 + -37d = 18 + -20d Solving -84 + -37d = 18 + -20d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '20d' to each side of the equation. -84 + -37d + 20d = 18 + -20d + 20d Combine like terms: -37d + 20d = -17d -84 + -17d = 18 + -20d + 20d Combine like terms: -20d + 20d = 0 -84 + -17d = 18 + 0 -84 + -17d = 18 Add '84' to each side of the equation. -84 + 84 + -17d = 18 + 84 Combine like terms: -84 + 84 = 0 0 + -17d = 18 + 84 -17d = 18 + 84 Combine like terms: 18 + 84 = 102 -17d = 102 Divide each side by '-17'. d = -6 Simplifying d = -6
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