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Simplifying 8(3a + -1b) + -3(8b + -2a) = 0 (3a * 8 + -1b * 8) + -3(8b + -2a) = 0 (24a + -8b) + -3(8b + -2a) = 0 Reorder the terms: 24a + -8b + -3(-2a + 8b) = 0 24a + -8b + (-2a * -3 + 8b * -3) = 0 24a + -8b + (6a + -24b) = 0 Reorder the terms: 24a + 6a + -8b + -24b = 0 Combine like terms: 24a + 6a = 30a 30a + -8b + -24b = 0 Combine like terms: -8b + -24b = -32b 30a + -32b = 0 Solving 30a + -32b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '32b' to each side of the equation. 30a + -32b + 32b = 0 + 32b Combine like terms: -32b + 32b = 0 30a + 0 = 0 + 32b 30a = 0 + 32b Remove the zero: 30a = 32b Divide each side by '30'. a = 1.066666667b Simplifying a = 1.066666667b
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