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Simplifying 2(2d + 1) + -3 = 5(3d + -9) + 4d Reorder the terms: 2(1 + 2d) + -3 = 5(3d + -9) + 4d (1 * 2 + 2d * 2) + -3 = 5(3d + -9) + 4d (2 + 4d) + -3 = 5(3d + -9) + 4d Reorder the terms: 2 + -3 + 4d = 5(3d + -9) + 4d Combine like terms: 2 + -3 = -1 -1 + 4d = 5(3d + -9) + 4d Reorder the terms: -1 + 4d = 5(-9 + 3d) + 4d -1 + 4d = (-9 * 5 + 3d * 5) + 4d -1 + 4d = (-45 + 15d) + 4d Combine like terms: 15d + 4d = 19d -1 + 4d = -45 + 19d Solving -1 + 4d = -45 + 19d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-19d' to each side of the equation. -1 + 4d + -19d = -45 + 19d + -19d Combine like terms: 4d + -19d = -15d -1 + -15d = -45 + 19d + -19d Combine like terms: 19d + -19d = 0 -1 + -15d = -45 + 0 -1 + -15d = -45 Add '1' to each side of the equation. -1 + 1 + -15d = -45 + 1 Combine like terms: -1 + 1 = 0 0 + -15d = -45 + 1 -15d = -45 + 1 Combine like terms: -45 + 1 = -44 -15d = -44 Divide each side by '-15'. d = 2.933333333 Simplifying d = 2.933333333
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