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Simplifying 7(2 + 5[1 + 2(2a + 3b)]) = 0 7(2 + 5[1 + (2a * 2 + 3b * 2)]) = 0 7(2 + 5[1 + (4a + 6b)]) = 0 7(2 + [1 * 5 + 4a * 5 + 6b * 5]) = 0 7(2 + [5 + 20a + 30b]) = 0 Combine like terms: 2 + 5 = 7 7(7 + 20a + 30b) = 0 (7 * 7 + 20a * 7 + 30b * 7) = 0 (49 + 140a + 210b) = 0 Solving 49 + 140a + 210b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + 140a + -49 + 210b = 0 + -49 Reorder the terms: 49 + -49 + 140a + 210b = 0 + -49 Combine like terms: 49 + -49 = 0 0 + 140a + 210b = 0 + -49 140a + 210b = 0 + -49 Combine like terms: 0 + -49 = -49 140a + 210b = -49 Add '-210b' to each side of the equation. 140a + 210b + -210b = -49 + -210b Combine like terms: 210b + -210b = 0 140a + 0 = -49 + -210b 140a = -49 + -210b Divide each side by '140'. a = -0.35 + -1.5b Simplifying a = -0.35 + -1.5b
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