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Simplifying x(a + -1b) + 2 = c(x + 3) + -1d (a * x + -1b * x) + 2 = c(x + 3) + -1d (ax + -1bx) + 2 = c(x + 3) + -1d Reorder the terms: 2 + ax + -1bx = c(x + 3) + -1d Reorder the terms: 2 + ax + -1bx = c(3 + x) + -1d 2 + ax + -1bx = (3 * c + x * c) + -1d 2 + ax + -1bx = (3c + cx) + -1d Solving 2 + ax + -1bx = 3c + cx + -1d Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + ax + -2 + -1bx = 3c + cx + -2 + -1d Reorder the terms: 2 + -2 + ax + -1bx = 3c + cx + -2 + -1d Combine like terms: 2 + -2 = 0 0 + ax + -1bx = 3c + cx + -2 + -1d ax + -1bx = 3c + cx + -2 + -1d Reorder the terms: ax + -1bx = -2 + 3c + cx + -1d Add 'bx' to each side of the equation. ax + -1bx + bx = -2 + 3c + cx + bx + -1d Combine like terms: -1bx + bx = 0 ax + 0 = -2 + 3c + cx + bx + -1d ax = -2 + 3c + cx + bx + -1d Reorder the terms: ax = -2 + bx + 3c + cx + -1d Divide each side by 'x'. a = -2x-1 + b + 3cx-1 + c + -1dx-1 Simplifying a = -2x-1 + b + 3cx-1 + c + -1dx-1 Reorder the terms: a = b + c + 3cx-1 + -1dx-1 + -2x-1
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