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