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Simplifying a(x + 1) + b(x + 1) = x(a + 2b) Reorder the terms: a(1 + x) + b(x + 1) = x(a + 2b) (1 * a + x * a) + b(x + 1) = x(a + 2b) (1a + ax) + b(x + 1) = x(a + 2b) Reorder the terms: 1a + ax + b(1 + x) = x(a + 2b) 1a + ax + (1 * b + x * b) = x(a + 2b) 1a + ax + (1b + bx) = x(a + 2b) 1a + ax + 1b + bx = (a * x + 2b * x) 1a + ax + 1b + bx = (ax + 2bx) Add '-1ax' to each side of the equation. 1a + ax + 1b + -1ax + bx = ax + -1ax + 2bx Reorder the terms: 1a + ax + -1ax + 1b + bx = ax + -1ax + 2bx Combine like terms: ax + -1ax = 0 1a + 0 + 1b + bx = ax + -1ax + 2bx 1a + 1b + bx = ax + -1ax + 2bx Combine like terms: ax + -1ax = 0 1a + 1b + bx = 0 + 2bx 1a + 1b + bx = 2bx Solving 1a + 1b + bx = 2bx 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. 1a + 1b + -1b + bx = -1b + 2bx Combine like terms: 1b + -1b = 0 1a + 0 + bx = -1b + 2bx 1a + bx = -1b + 2bx Add '-1bx' to each side of the equation. 1a + bx + -1bx = -1b + 2bx + -1bx Combine like terms: bx + -1bx = 0 1a + 0 = -1b + 2bx + -1bx 1a = -1b + 2bx + -1bx Combine like terms: 2bx + -1bx = 1bx 1a = -1b + 1bx Divide each side by '1'. a = -1b + 1bx Simplifying a = -1b + 1bx
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