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Simplifying (a + -1b) * x + (a + -1b) * x = 2a Reorder the terms for easier multiplication: x(a + -1b) + (a + -1b) * x = 2a (a * x + -1b * x) + (a + -1b) * x = 2a (ax + -1bx) + (a + -1b) * x = 2a Reorder the terms for easier multiplication: ax + -1bx + x(a + -1b) = 2a ax + -1bx + (a * x + -1b * x) = 2a ax + -1bx + (ax + -1bx) = 2a Reorder the terms: ax + ax + -1bx + -1bx = 2a Combine like terms: ax + ax = 2ax 2ax + -1bx + -1bx = 2a Combine like terms: -1bx + -1bx = -2bx 2ax + -2bx = 2a Solving 2ax + -2bx = 2a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 2ax + -2a + -2bx = 2a + -2a Reorder the terms: -2a + 2ax + -2bx = 2a + -2a Combine like terms: 2a + -2a = 0 -2a + 2ax + -2bx = 0 Add '2bx' to each side of the equation. -2a + 2ax + -2bx + 2bx = 0 + 2bx Combine like terms: -2bx + 2bx = 0 -2a + 2ax + 0 = 0 + 2bx -2a + 2ax = 0 + 2bx Remove the zero: -2a + 2ax = 2bx Combine like terms: 2bx + -2bx = 0 -2a + 2ax + -2bx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1a + ax + -1bx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1a + ax + -1bx)' equal to zero and attempt to solve: Simplifying -1a + ax + -1bx = 0 Solving -1a + ax + -1bx = 0 Move all terms containing a to the left, all other terms to the right. Add 'bx' to each side of the equation. -1a + ax + -1bx + bx = 0 + bx Combine like terms: -1bx + bx = 0 -1a + ax + 0 = 0 + bx -1a + ax = 0 + bx Remove the zero: -1a + ax = bx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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