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Simplifying 5(4a + 3b) + 3(a + -1b) = 0 (4a * 5 + 3b * 5) + 3(a + -1b) = 0 (20a + 15b) + 3(a + -1b) = 0 20a + 15b + (a * 3 + -1b * 3) = 0 20a + 15b + (3a + -3b) = 0 Reorder the terms: 20a + 3a + 15b + -3b = 0 Combine like terms: 20a + 3a = 23a 23a + 15b + -3b = 0 Combine like terms: 15b + -3b = 12b 23a + 12b = 0 Solving 23a + 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. 23a + 12b + -12b = 0 + -12b Combine like terms: 12b + -12b = 0 23a + 0 = 0 + -12b 23a = 0 + -12b Remove the zero: 23a = -12b Divide each side by '23'. a = -0.5217391304b Simplifying a = -0.5217391304b
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