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Simplifying 7(d + -5) + 12 = 5 + 3d Reorder the terms: 7(-5 + d) + 12 = 5 + 3d (-5 * 7 + d * 7) + 12 = 5 + 3d (-35 + 7d) + 12 = 5 + 3d Reorder the terms: -35 + 12 + 7d = 5 + 3d Combine like terms: -35 + 12 = -23 -23 + 7d = 5 + 3d Solving -23 + 7d = 5 + 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. -23 + 7d + -3d = 5 + 3d + -3d Combine like terms: 7d + -3d = 4d -23 + 4d = 5 + 3d + -3d Combine like terms: 3d + -3d = 0 -23 + 4d = 5 + 0 -23 + 4d = 5 Add '23' to each side of the equation. -23 + 23 + 4d = 5 + 23 Combine like terms: -23 + 23 = 0 0 + 4d = 5 + 23 4d = 5 + 23 Combine like terms: 5 + 23 = 28 4d = 28 Divide each side by '4'. d = 7 Simplifying d = 7
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