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Simplifying 5(d + -3) + -2(d + 4) = d + -7 Reorder the terms: 5(-3 + d) + -2(d + 4) = d + -7 (-3 * 5 + d * 5) + -2(d + 4) = d + -7 (-15 + 5d) + -2(d + 4) = d + -7 Reorder the terms: -15 + 5d + -2(4 + d) = d + -7 -15 + 5d + (4 * -2 + d * -2) = d + -7 -15 + 5d + (-8 + -2d) = d + -7 Reorder the terms: -15 + -8 + 5d + -2d = d + -7 Combine like terms: -15 + -8 = -23 -23 + 5d + -2d = d + -7 Combine like terms: 5d + -2d = 3d -23 + 3d = d + -7 Reorder the terms: -23 + 3d = -7 + d Solving -23 + 3d = -7 + d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1d' to each side of the equation. -23 + 3d + -1d = -7 + d + -1d Combine like terms: 3d + -1d = 2d -23 + 2d = -7 + d + -1d Combine like terms: d + -1d = 0 -23 + 2d = -7 + 0 -23 + 2d = -7 Add '23' to each side of the equation. -23 + 23 + 2d = -7 + 23 Combine like terms: -23 + 23 = 0 0 + 2d = -7 + 23 2d = -7 + 23 Combine like terms: -7 + 23 = 16 2d = 16 Divide each side by '2'. d = 8 Simplifying d = 8
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