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Simplifying 5(4a + -3b) + -1(4a + -3b) = 0 (4a * 5 + -3b * 5) + -1(4a + -3b) = 0 (20a + -15b) + -1(4a + -3b) = 0 20a + -15b + (4a * -1 + -3b * -1) = 0 20a + -15b + (-4a + 3b) = 0 Reorder the terms: 20a + -4a + -15b + 3b = 0 Combine like terms: 20a + -4a = 16a 16a + -15b + 3b = 0 Combine like terms: -15b + 3b = -12b 16a + -12b = 0 Solving 16a + -12b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12b' to each side of the equation. 16a + -12b + 12b = 0 + 12b Combine like terms: -12b + 12b = 0 16a + 0 = 0 + 12b 16a = 0 + 12b Remove the zero: 16a = 12b Divide each side by '16'. a = 0.75b Simplifying a = 0.75b
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