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Simplifying 7(3a + 4b) + 7(5a + b) = 0 (3a * 7 + 4b * 7) + 7(5a + b) = 0 (21a + 28b) + 7(5a + b) = 0 21a + 28b + (5a * 7 + b * 7) = 0 21a + 28b + (35a + 7b) = 0 Reorder the terms: 21a + 35a + 28b + 7b = 0 Combine like terms: 21a + 35a = 56a 56a + 28b + 7b = 0 Combine like terms: 28b + 7b = 35b 56a + 35b = 0 Solving 56a + 35b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-35b' to each side of the equation. 56a + 35b + -35b = 0 + -35b Combine like terms: 35b + -35b = 0 56a + 0 = 0 + -35b 56a = 0 + -35b Remove the zero: 56a = -35b Divide each side by '56'. a = -0.625b Simplifying a = -0.625b
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