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Simplifying 5(2a + -3b) + -3(a + -1b) = 0 (2a * 5 + -3b * 5) + -3(a + -1b) = 0 (10a + -15b) + -3(a + -1b) = 0 10a + -15b + (a * -3 + -1b * -3) = 0 10a + -15b + (-3a + 3b) = 0 Reorder the terms: 10a + -3a + -15b + 3b = 0 Combine like terms: 10a + -3a = 7a 7a + -15b + 3b = 0 Combine like terms: -15b + 3b = -12b 7a + -12b = 0 Solving 7a + -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. 7a + -12b + 12b = 0 + 12b Combine like terms: -12b + 12b = 0 7a + 0 = 0 + 12b 7a = 0 + 12b Remove the zero: 7a = 12b Divide each side by '7'. a = 1.714285714b Simplifying a = 1.714285714b
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