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Simplifying 42 + 9d = 5(9d + -6) Reorder the terms: 42 + 9d = 5(-6 + 9d) 42 + 9d = (-6 * 5 + 9d * 5) 42 + 9d = (-30 + 45d) Solving 42 + 9d = -30 + 45d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-45d' to each side of the equation. 42 + 9d + -45d = -30 + 45d + -45d Combine like terms: 9d + -45d = -36d 42 + -36d = -30 + 45d + -45d Combine like terms: 45d + -45d = 0 42 + -36d = -30 + 0 42 + -36d = -30 Add '-42' to each side of the equation. 42 + -42 + -36d = -30 + -42 Combine like terms: 42 + -42 = 0 0 + -36d = -30 + -42 -36d = -30 + -42 Combine like terms: -30 + -42 = -72 -36d = -72 Divide each side by '-36'. d = 2 Simplifying d = 2
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