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Simplifying 7(5a + -1b) + -7(2b + -7a) = 0 (5a * 7 + -1b * 7) + -7(2b + -7a) = 0 (35a + -7b) + -7(2b + -7a) = 0 Reorder the terms: 35a + -7b + -7(-7a + 2b) = 0 35a + -7b + (-7a * -7 + 2b * -7) = 0 35a + -7b + (49a + -14b) = 0 Reorder the terms: 35a + 49a + -7b + -14b = 0 Combine like terms: 35a + 49a = 84a 84a + -7b + -14b = 0 Combine like terms: -7b + -14b = -21b 84a + -21b = 0 Solving 84a + -21b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '21b' to each side of the equation. 84a + -21b + 21b = 0 + 21b Combine like terms: -21b + 21b = 0 84a + 0 = 0 + 21b 84a = 0 + 21b Remove the zero: 84a = 21b Divide each side by '84'. a = 0.25b Simplifying a = 0.25b
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