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Simplifying 3(6a + -1b) + -7(5b + -2a) = 0 (6a * 3 + -1b * 3) + -7(5b + -2a) = 0 (18a + -3b) + -7(5b + -2a) = 0 Reorder the terms: 18a + -3b + -7(-2a + 5b) = 0 18a + -3b + (-2a * -7 + 5b * -7) = 0 18a + -3b + (14a + -35b) = 0 Reorder the terms: 18a + 14a + -3b + -35b = 0 Combine like terms: 18a + 14a = 32a 32a + -3b + -35b = 0 Combine like terms: -3b + -35b = -38b 32a + -38b = 0 Solving 32a + -38b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '38b' to each side of the equation. 32a + -38b + 38b = 0 + 38b Combine like terms: -38b + 38b = 0 32a + 0 = 0 + 38b 32a = 0 + 38b Remove the zero: 32a = 38b Divide each side by '32'. a = 1.1875b Simplifying a = 1.1875b
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