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Simplifying 7(4a + -1b) + -8(2b + -8a) = 0 (4a * 7 + -1b * 7) + -8(2b + -8a) = 0 (28a + -7b) + -8(2b + -8a) = 0 Reorder the terms: 28a + -7b + -8(-8a + 2b) = 0 28a + -7b + (-8a * -8 + 2b * -8) = 0 28a + -7b + (64a + -16b) = 0 Reorder the terms: 28a + 64a + -7b + -16b = 0 Combine like terms: 28a + 64a = 92a 92a + -7b + -16b = 0 Combine like terms: -7b + -16b = -23b 92a + -23b = 0 Solving 92a + -23b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '23b' to each side of the equation. 92a + -23b + 23b = 0 + 23b Combine like terms: -23b + 23b = 0 92a + 0 = 0 + 23b 92a = 0 + 23b Remove the zero: 92a = 23b Divide each side by '92'. a = 0.25b Simplifying a = 0.25b
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