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Simplifying (5a + -1b) * x + b + 2c = 0 Reorder the terms for easier multiplication: x(5a + -1b) + b + 2c = 0 (5a * x + -1b * x) + b + 2c = 0 (5ax + -1bx) + b + 2c = 0 Reorder the terms: 5ax + b + -1bx + 2c = 0 Solving 5ax + b + -1bx + 2c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 5ax + b + -1bx + -1b + 2c = 0 + -1b Reorder the terms: 5ax + b + -1b + -1bx + 2c = 0 + -1b Combine like terms: b + -1b = 0 5ax + 0 + -1bx + 2c = 0 + -1b 5ax + -1bx + 2c = 0 + -1b Remove the zero: 5ax + -1bx + 2c = -1b Add 'bx' to each side of the equation. 5ax + -1bx + bx + 2c = -1b + bx Combine like terms: -1bx + bx = 0 5ax + 0 + 2c = -1b + bx 5ax + 2c = -1b + bx Add '-2c' to each side of the equation. 5ax + 2c + -2c = -1b + bx + -2c Combine like terms: 2c + -2c = 0 5ax + 0 = -1b + bx + -2c 5ax = -1b + bx + -2c Divide each side by '5x'. a = -0.2bx-1 + 0.2b + -0.4cx-1 Simplifying a = -0.2bx-1 + 0.2b + -0.4cx-1 Reorder the terms: a = 0.2b + -0.2bx-1 + -0.4cx-1
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