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Simplifying 0.45(d + -1) = 1.5(4d + 3) + 1 Reorder the terms: 0.45(-1 + d) = 1.5(4d + 3) + 1 (-1 * 0.45 + d * 0.45) = 1.5(4d + 3) + 1 (-0.45 + 0.45d) = 1.5(4d + 3) + 1 Reorder the terms: -0.45 + 0.45d = 1.5(3 + 4d) + 1 -0.45 + 0.45d = (3 * 1.5 + 4d * 1.5) + 1 -0.45 + 0.45d = (4.5 + 6d) + 1 Reorder the terms: -0.45 + 0.45d = 4.5 + 1 + 6d Combine like terms: 4.5 + 1 = 5.5 -0.45 + 0.45d = 5.5 + 6d Solving -0.45 + 0.45d = 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. -0.45 + 0.45d + -6d = 5.5 + 6d + -6d Combine like terms: 0.45d + -6d = -5.55d -0.45 + -5.55d = 5.5 + 6d + -6d Combine like terms: 6d + -6d = 0 -0.45 + -5.55d = 5.5 + 0 -0.45 + -5.55d = 5.5 Add '0.45' to each side of the equation. -0.45 + 0.45 + -5.55d = 5.5 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + -5.55d = 5.5 + 0.45 -5.55d = 5.5 + 0.45 Combine like terms: 5.5 + 0.45 = 5.95 -5.55d = 5.95 Divide each side by '-5.55'. d = -1.072072072 Simplifying d = -1.072072072
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