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Simplifying (x + 1)(1 + a) = 2ax + -1a(x + -3) Reorder the terms: (1 + x)(1 + a) = 2ax + -1a(x + -3) Multiply (1 + x) * (1 + a) (1(1 + a) + x(1 + a)) = 2ax + -1a(x + -3) ((1 * 1 + a * 1) + x(1 + a)) = 2ax + -1a(x + -3) ((1 + 1a) + x(1 + a)) = 2ax + -1a(x + -3) (1 + 1a + (1 * x + a * x)) = 2ax + -1a(x + -3) Reorder the terms: (1 + 1a + (ax + 1x)) = 2ax + -1a(x + -3) (1 + 1a + (ax + 1x)) = 2ax + -1a(x + -3) (1 + 1a + ax + 1x) = 2ax + -1a(x + -3) Reorder the terms: 1 + 1a + ax + 1x = 2ax + -1a(-3 + x) 1 + 1a + ax + 1x = 2ax + (-3 * -1a + x * -1a) 1 + 1a + ax + 1x = 2ax + (3a + -1ax) Reorder the terms: 1 + 1a + ax + 1x = 3a + 2ax + -1ax Combine like terms: 2ax + -1ax = 1ax 1 + 1a + ax + 1x = 3a + 1ax Solving 1 + 1a + ax + 1x = 3a + 1ax Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3a' to each side of the equation. 1 + 1a + ax + -3a + 1x = 3a + -3a + 1ax Reorder the terms: 1 + 1a + -3a + ax + 1x = 3a + -3a + 1ax Combine like terms: 1a + -3a = -2a 1 + -2a + ax + 1x = 3a + -3a + 1ax Combine like terms: 3a + -3a = 0 1 + -2a + ax + 1x = 0 + 1ax 1 + -2a + ax + 1x = 1ax Add '-1ax' to each side of the equation. 1 + -2a + ax + -1ax + 1x = 1ax + -1ax Combine like terms: ax + -1ax = 0 1 + -2a + 0 + 1x = 1ax + -1ax 1 + -2a + 1x = 1ax + -1ax Combine like terms: 1ax + -1ax = 0 1 + -2a + 1x = 0 Add '-1' to each side of the equation. 1 + -2a + -1 + 1x = 0 + -1 Reorder the terms: 1 + -1 + -2a + 1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a + 1x = 0 + -1 -2a + 1x = 0 + -1 Combine like terms: 0 + -1 = -1 -2a + 1x = -1 Add '-1x' to each side of the equation. -2a + 1x + -1x = -1 + -1x Combine like terms: 1x + -1x = 0 -2a + 0 = -1 + -1x -2a = -1 + -1x Divide each side by '-2'. a = 0.5 + 0.5x Simplifying a = 0.5 + 0.5x
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