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Simplifying 5 + -1(8 + -1d) + -52 = 19d + -6(2 + 4d) 5 + (8 * -1 + -1d * -1) + -52 = 19d + -6(2 + 4d) 5 + (-8 + 1d) + -52 = 19d + -6(2 + 4d) Reorder the terms: 5 + -8 + -52 + 1d = 19d + -6(2 + 4d) Combine like terms: 5 + -8 = -3 -3 + -52 + 1d = 19d + -6(2 + 4d) Combine like terms: -3 + -52 = -55 -55 + 1d = 19d + -6(2 + 4d) -55 + 1d = 19d + (2 * -6 + 4d * -6) -55 + 1d = 19d + (-12 + -24d) Reorder the terms: -55 + 1d = -12 + 19d + -24d Combine like terms: 19d + -24d = -5d -55 + 1d = -12 + -5d Solving -55 + 1d = -12 + -5d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5d' to each side of the equation. -55 + 1d + 5d = -12 + -5d + 5d Combine like terms: 1d + 5d = 6d -55 + 6d = -12 + -5d + 5d Combine like terms: -5d + 5d = 0 -55 + 6d = -12 + 0 -55 + 6d = -12 Add '55' to each side of the equation. -55 + 55 + 6d = -12 + 55 Combine like terms: -55 + 55 = 0 0 + 6d = -12 + 55 6d = -12 + 55 Combine like terms: -12 + 55 = 43 6d = 43 Divide each side by '6'. d = 7.166666667 Simplifying d = 7.166666667
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