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Simplifying 8(6a + -1b) + -4(8b + -8a) = 0 (6a * 8 + -1b * 8) + -4(8b + -8a) = 0 (48a + -8b) + -4(8b + -8a) = 0 Reorder the terms: 48a + -8b + -4(-8a + 8b) = 0 48a + -8b + (-8a * -4 + 8b * -4) = 0 48a + -8b + (32a + -32b) = 0 Reorder the terms: 48a + 32a + -8b + -32b = 0 Combine like terms: 48a + 32a = 80a 80a + -8b + -32b = 0 Combine like terms: -8b + -32b = -40b 80a + -40b = 0 Solving 80a + -40b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '40b' to each side of the equation. 80a + -40b + 40b = 0 + 40b Combine like terms: -40b + 40b = 0 80a + 0 = 0 + 40b 80a = 0 + 40b Remove the zero: 80a = 40b Divide each side by '80'. a = 0.5b Simplifying a = 0.5b
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