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Simplifying 5(2 + -1d) = 7(d + -5) + 7d (2 * 5 + -1d * 5) = 7(d + -5) + 7d (10 + -5d) = 7(d + -5) + 7d Reorder the terms: 10 + -5d = 7(-5 + d) + 7d 10 + -5d = (-5 * 7 + d * 7) + 7d 10 + -5d = (-35 + 7d) + 7d Combine like terms: 7d + 7d = 14d 10 + -5d = -35 + 14d Solving 10 + -5d = -35 + 14d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-14d' to each side of the equation. 10 + -5d + -14d = -35 + 14d + -14d Combine like terms: -5d + -14d = -19d 10 + -19d = -35 + 14d + -14d Combine like terms: 14d + -14d = 0 10 + -19d = -35 + 0 10 + -19d = -35 Add '-10' to each side of the equation. 10 + -10 + -19d = -35 + -10 Combine like terms: 10 + -10 = 0 0 + -19d = -35 + -10 -19d = -35 + -10 Combine like terms: -35 + -10 = -45 -19d = -45 Divide each side by '-19'. d = 2.368421053 Simplifying d = 2.368421053
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