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Simplifying 0.25(d + -1) = 1.5(4d + 3) + 1 Reorder the terms: 0.25(-1 + d) = 1.5(4d + 3) + 1 (-1 * 0.25 + d * 0.25) = 1.5(4d + 3) + 1 (-0.25 + 0.25d) = 1.5(4d + 3) + 1 Reorder the terms: -0.25 + 0.25d = 1.5(3 + 4d) + 1 -0.25 + 0.25d = (3 * 1.5 + 4d * 1.5) + 1 -0.25 + 0.25d = (4.5 + 6d) + 1 Reorder the terms: -0.25 + 0.25d = 4.5 + 1 + 6d Combine like terms: 4.5 + 1 = 5.5 -0.25 + 0.25d = 5.5 + 6d Solving -0.25 + 0.25d = 5.5 + 6d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6d' to each side of the equation. -0.25 + 0.25d + -6d = 5.5 + 6d + -6d Combine like terms: 0.25d + -6d = -5.75d -0.25 + -5.75d = 5.5 + 6d + -6d Combine like terms: 6d + -6d = 0 -0.25 + -5.75d = 5.5 + 0 -0.25 + -5.75d = 5.5 Add '0.25' to each side of the equation. -0.25 + 0.25 + -5.75d = 5.5 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -5.75d = 5.5 + 0.25 -5.75d = 5.5 + 0.25 Combine like terms: 5.5 + 0.25 = 5.75 -5.75d = 5.75 Divide each side by '-5.75'. d = -1 Simplifying d = -1
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