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Simplifying 5(3a + -1b) + -4(2a + -2b) = 0 (3a * 5 + -1b * 5) + -4(2a + -2b) = 0 (15a + -5b) + -4(2a + -2b) = 0 15a + -5b + (2a * -4 + -2b * -4) = 0 15a + -5b + (-8a + 8b) = 0 Reorder the terms: 15a + -8a + -5b + 8b = 0 Combine like terms: 15a + -8a = 7a 7a + -5b + 8b = 0 Combine like terms: -5b + 8b = 3b 7a + 3b = 0 Solving 7a + 3b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 7a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 7a + 0 = 0 + -3b 7a = 0 + -3b Remove the zero: 7a = -3b Divide each side by '7'. a = -0.4285714286b Simplifying a = -0.4285714286b
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