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Simplifying a + -3d + a + -1d + a + d + a + -3d = 12 Reorder the terms: a + a + a + a + -3d + -1d + d + -3d = 12 Combine like terms: a + a = 2a 2a + a + a + -3d + -1d + d + -3d = 12 Combine like terms: 2a + a = 3a 3a + a + -3d + -1d + d + -3d = 12 Combine like terms: 3a + a = 4a 4a + -3d + -1d + d + -3d = 12 Combine like terms: -3d + -1d = -4d 4a + -4d + d + -3d = 12 Combine like terms: -4d + d = -3d 4a + -3d + -3d = 12 Combine like terms: -3d + -3d = -6d 4a + -6d = 12 Solving 4a + -6d = 12 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6d' to each side of the equation. 4a + -6d + 6d = 12 + 6d Combine like terms: -6d + 6d = 0 4a + 0 = 12 + 6d 4a = 12 + 6d Divide each side by '4'. a = 3 + 1.5d Simplifying a = 3 + 1.5d
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