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Simplifying -6(2d + -3) + -5(8 + -3d) = 7(5 + -3x) Reorder the terms: -6(-3 + 2d) + -5(8 + -3d) = 7(5 + -3x) (-3 * -6 + 2d * -6) + -5(8 + -3d) = 7(5 + -3x) (18 + -12d) + -5(8 + -3d) = 7(5 + -3x) 18 + -12d + (8 * -5 + -3d * -5) = 7(5 + -3x) 18 + -12d + (-40 + 15d) = 7(5 + -3x) Reorder the terms: 18 + -40 + -12d + 15d = 7(5 + -3x) Combine like terms: 18 + -40 = -22 -22 + -12d + 15d = 7(5 + -3x) Combine like terms: -12d + 15d = 3d -22 + 3d = 7(5 + -3x) -22 + 3d = (5 * 7 + -3x * 7) -22 + 3d = (35 + -21x) Solving -22 + 3d = 35 + -21x Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + 3d = 35 + 22 + -21x Combine like terms: -22 + 22 = 0 0 + 3d = 35 + 22 + -21x 3d = 35 + 22 + -21x Combine like terms: 35 + 22 = 57 3d = 57 + -21x Divide each side by '3'. d = 19 + -7x Simplifying d = 19 + -7x
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