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Simplifying 17d + -9(2 + -1a) = 12a + 1d 17d + (2 * -9 + -1a * -9) = 12a + 1d 17d + (-18 + 9a) = 12a + 1d Reorder the terms: -18 + 9a + 17d = 12a + 1d Solving -18 + 9a + 17d = 12a + 1d Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12a' to each side of the equation. -18 + 9a + -12a + 17d = 12a + -12a + 1d Combine like terms: 9a + -12a = -3a -18 + -3a + 17d = 12a + -12a + 1d Combine like terms: 12a + -12a = 0 -18 + -3a + 17d = 0 + 1d -18 + -3a + 17d = 1d Add '18' to each side of the equation. -18 + -3a + 18 + 17d = 18 + 1d Reorder the terms: -18 + 18 + -3a + 17d = 18 + 1d Combine like terms: -18 + 18 = 0 0 + -3a + 17d = 18 + 1d -3a + 17d = 18 + 1d Add '-17d' to each side of the equation. -3a + 17d + -17d = 18 + 1d + -17d Combine like terms: 17d + -17d = 0 -3a + 0 = 18 + 1d + -17d -3a = 18 + 1d + -17d Combine like terms: 1d + -17d = -16d -3a = 18 + -16d Divide each side by '-3'. a = -6 + 5.333333333d Simplifying a = -6 + 5.333333333d
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