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Simplifying (3a + 1) * x + (a + 2) * x + 1 = 0 Reorder the terms: (1 + 3a) * x + (a + 2) * x + 1 = 0 Reorder the terms for easier multiplication: x(1 + 3a) + (a + 2) * x + 1 = 0 (1 * x + 3a * x) + (a + 2) * x + 1 = 0 Reorder the terms: (3ax + 1x) + (a + 2) * x + 1 = 0 (3ax + 1x) + (a + 2) * x + 1 = 0 Reorder the terms: 3ax + 1x + (2 + a) * x + 1 = 0 Reorder the terms for easier multiplication: 3ax + 1x + x(2 + a) + 1 = 0 3ax + 1x + (2 * x + a * x) + 1 = 0 Reorder the terms: 3ax + 1x + (ax + 2x) + 1 = 0 3ax + 1x + (ax + 2x) + 1 = 0 Reorder the terms: 1 + 3ax + ax + 1x + 2x = 0 Combine like terms: 3ax + ax = 4ax 1 + 4ax + 1x + 2x = 0 Combine like terms: 1x + 2x = 3x 1 + 4ax + 3x = 0 Solving 1 + 4ax + 3x = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 4ax + -1 + 3x = 0 + -1 Reorder the terms: 1 + -1 + 4ax + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4ax + 3x = 0 + -1 4ax + 3x = 0 + -1 Combine like terms: 0 + -1 = -1 4ax + 3x = -1 Add '-3x' to each side of the equation. 4ax + 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 4ax + 0 = -1 + -3x 4ax = -1 + -3x Divide each side by '4x'. a = -0.25x-1 + -0.75 Simplifying a = -0.25x-1 + -0.75 Reorder the terms: a = -0.75 + -0.25x-1
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