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Simplifying (a + b) * t + 2a + -1b = 8 Reorder the terms for easier multiplication: t(a + b) + 2a + -1b = 8 (a * t + b * t) + 2a + -1b = 8 (at + bt) + 2a + -1b = 8 Reorder the terms: 2a + at + -1b + bt = 8 Solving 2a + at + -1b + bt = 8 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + at + -1b + b + bt = 8 + b Combine like terms: -1b + b = 0 2a + at + 0 + bt = 8 + b 2a + at + bt = 8 + b Add '-1bt' to each side of the equation. 2a + at + bt + -1bt = 8 + b + -1bt Combine like terms: bt + -1bt = 0 2a + at + 0 = 8 + b + -1bt 2a + at = 8 + b + -1bt Reorder the terms: -8 + 2a + at + -1b + bt = 8 + b + -1bt + -8 + -1b + bt Reorder the terms: -8 + 2a + at + -1b + bt = 8 + -8 + b + -1b + -1bt + bt Combine like terms: 8 + -8 = 0 -8 + 2a + at + -1b + bt = 0 + b + -1b + -1bt + bt -8 + 2a + at + -1b + bt = b + -1b + -1bt + bt Combine like terms: b + -1b = 0 -8 + 2a + at + -1b + bt = 0 + -1bt + bt -8 + 2a + at + -1b + bt = -1bt + bt Combine like terms: -1bt + bt = 0 -8 + 2a + at + -1b + bt = 0 The solution to this equation could not be determined.
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