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Simplifying 5(a + -1b) + 6(a + b) + -7(a + -2b) = 0 (a * 5 + -1b * 5) + 6(a + b) + -7(a + -2b) = 0 (5a + -5b) + 6(a + b) + -7(a + -2b) = 0 5a + -5b + (a * 6 + b * 6) + -7(a + -2b) = 0 5a + -5b + (6a + 6b) + -7(a + -2b) = 0 5a + -5b + 6a + 6b + (a * -7 + -2b * -7) = 0 5a + -5b + 6a + 6b + (-7a + 14b) = 0 Reorder the terms: 5a + 6a + -7a + -5b + 6b + 14b = 0 Combine like terms: 5a + 6a = 11a 11a + -7a + -5b + 6b + 14b = 0 Combine like terms: 11a + -7a = 4a 4a + -5b + 6b + 14b = 0 Combine like terms: -5b + 6b = 1b 4a + 1b + 14b = 0 Combine like terms: 1b + 14b = 15b 4a + 15b = 0 Solving 4a + 15b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-15b' to each side of the equation. 4a + 15b + -15b = 0 + -15b Combine like terms: 15b + -15b = 0 4a + 0 = 0 + -15b 4a = 0 + -15b Remove the zero: 4a = -15b Divide each side by '4'. a = -3.75b Simplifying a = -3.75b
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