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Simplifying 7(d + -5) + 8 = (3d + -8) + 1 Reorder the terms: 7(-5 + d) + 8 = (3d + -8) + 1 (-5 * 7 + d * 7) + 8 = (3d + -8) + 1 (-35 + 7d) + 8 = (3d + -8) + 1 Reorder the terms: -35 + 8 + 7d = (3d + -8) + 1 Combine like terms: -35 + 8 = -27 -27 + 7d = (3d + -8) + 1 Reorder the terms: -27 + 7d = (-8 + 3d) + 1 Remove parenthesis around (-8 + 3d) -27 + 7d = -8 + 3d + 1 Reorder the terms: -27 + 7d = -8 + 1 + 3d Combine like terms: -8 + 1 = -7 -27 + 7d = -7 + 3d Solving -27 + 7d = -7 + 3d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3d' to each side of the equation. -27 + 7d + -3d = -7 + 3d + -3d Combine like terms: 7d + -3d = 4d -27 + 4d = -7 + 3d + -3d Combine like terms: 3d + -3d = 0 -27 + 4d = -7 + 0 -27 + 4d = -7 Add '27' to each side of the equation. -27 + 27 + 4d = -7 + 27 Combine like terms: -27 + 27 = 0 0 + 4d = -7 + 27 4d = -7 + 27 Combine like terms: -7 + 27 = 20 4d = 20 Divide each side by '4'. d = 5 Simplifying d = 5
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