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Simplifying 7(2a + 3b) + 4(a + 2b) = 0 (2a * 7 + 3b * 7) + 4(a + 2b) = 0 (14a + 21b) + 4(a + 2b) = 0 14a + 21b + (a * 4 + 2b * 4) = 0 14a + 21b + (4a + 8b) = 0 Reorder the terms: 14a + 4a + 21b + 8b = 0 Combine like terms: 14a + 4a = 18a 18a + 21b + 8b = 0 Combine like terms: 21b + 8b = 29b 18a + 29b = 0 Solving 18a + 29b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-29b' to each side of the equation. 18a + 29b + -29b = 0 + -29b Combine like terms: 29b + -29b = 0 18a + 0 = 0 + -29b 18a = 0 + -29b Remove the zero: 18a = -29b Divide each side by '18'. a = -1.611111111b Simplifying a = -1.611111111b
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