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Simplifying 7(2a + 3b) + 4(-5a + 2b) = 0 (2a * 7 + 3b * 7) + 4(-5a + 2b) = 0 (14a + 21b) + 4(-5a + 2b) = 0 14a + 21b + (-5a * 4 + 2b * 4) = 0 14a + 21b + (-20a + 8b) = 0 Reorder the terms: 14a + -20a + 21b + 8b = 0 Combine like terms: 14a + -20a = -6a -6a + 21b + 8b = 0 Combine like terms: 21b + 8b = 29b -6a + 29b = 0 Solving -6a + 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. -6a + 29b + -29b = 0 + -29b Combine like terms: 29b + -29b = 0 -6a + 0 = 0 + -29b -6a = 0 + -29b Remove the zero: -6a = -29b Divide each side by '-6'. a = 4.833333333b Simplifying a = 4.833333333b
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