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Simplifying 8(4a + -1b) + -5(7b + -2a) = 0 (4a * 8 + -1b * 8) + -5(7b + -2a) = 0 (32a + -8b) + -5(7b + -2a) = 0 Reorder the terms: 32a + -8b + -5(-2a + 7b) = 0 32a + -8b + (-2a * -5 + 7b * -5) = 0 32a + -8b + (10a + -35b) = 0 Reorder the terms: 32a + 10a + -8b + -35b = 0 Combine like terms: 32a + 10a = 42a 42a + -8b + -35b = 0 Combine like terms: -8b + -35b = -43b 42a + -43b = 0 Solving 42a + -43b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '43b' to each side of the equation. 42a + -43b + 43b = 0 + 43b Combine like terms: -43b + 43b = 0 42a + 0 = 0 + 43b 42a = 0 + 43b Remove the zero: 42a = 43b Divide each side by '42'. a = 1.023809524b Simplifying a = 1.023809524b
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