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Simplifying a + (2p + -1) * d = 50 + a + (p + -1) * d Reorder the terms: a + (-1 + 2p) * d = 50 + a + (p + -1) * d Reorder the terms for easier multiplication: a + d(-1 + 2p) = 50 + a + (p + -1) * d a + (-1 * d + 2p * d) = 50 + a + (p + -1) * d a + (-1d + 2dp) = 50 + a + (p + -1) * d Reorder the terms: a + -1d + 2dp = 50 + a + (-1 + p) * d Reorder the terms for easier multiplication: a + -1d + 2dp = 50 + a + d(-1 + p) a + -1d + 2dp = 50 + a + (-1 * d + p * d) a + -1d + 2dp = 50 + a + (-1d + dp) Add '-1a' to each side of the equation. a + -1d + -1a + 2dp = 50 + a + -1d + -1a + dp Reorder the terms: a + -1a + -1d + 2dp = 50 + a + -1d + -1a + dp Combine like terms: a + -1a = 0 0 + -1d + 2dp = 50 + a + -1d + -1a + dp -1d + 2dp = 50 + a + -1d + -1a + dp Reorder the terms: -1d + 2dp = 50 + a + -1a + -1d + dp Combine like terms: a + -1a = 0 -1d + 2dp = 50 + 0 + -1d + dp -1d + 2dp = 50 + -1d + dp Add 'd' to each side of the equation. -1d + d + 2dp = 50 + -1d + d + dp Combine like terms: -1d + d = 0 0 + 2dp = 50 + -1d + d + dp 2dp = 50 + -1d + d + dp Combine like terms: -1d + d = 0 2dp = 50 + 0 + dp 2dp = 50 + dp Solving 2dp = 50 + dp Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dp' to each side of the equation. 2dp + -1dp = 50 + dp + -1dp Combine like terms: 2dp + -1dp = 1dp 1dp = 50 + dp + -1dp Combine like terms: dp + -1dp = 0 1dp = 50 + 0 1dp = 50 Divide each side by '1p'. d = 50p-1 Simplifying d = 50p-1
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