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Simplifying 5(3a + 2b) + 4(-5a + b) = 0 (3a * 5 + 2b * 5) + 4(-5a + b) = 0 (15a + 10b) + 4(-5a + b) = 0 15a + 10b + (-5a * 4 + b * 4) = 0 15a + 10b + (-20a + 4b) = 0 Reorder the terms: 15a + -20a + 10b + 4b = 0 Combine like terms: 15a + -20a = -5a -5a + 10b + 4b = 0 Combine like terms: 10b + 4b = 14b -5a + 14b = 0 Solving -5a + 14b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14b' to each side of the equation. -5a + 14b + -14b = 0 + -14b Combine like terms: 14b + -14b = 0 -5a + 0 = 0 + -14b -5a = 0 + -14b Remove the zero: -5a = -14b Divide each side by '-5'. a = 2.8b Simplifying a = 2.8b
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