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Simplifying (2a + -6b + c + -9d) * 7 = 0 Reorder the terms for easier multiplication: 7(2a + -6b + c + -9d) = 0 (2a * 7 + -6b * 7 + c * 7 + -9d * 7) = 0 (14a + -42b + 7c + -63d) = 0 Solving 14a + -42b + 7c + -63d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '42b' to each side of the equation. 14a + -42b + 7c + 42b + -63d = 0 + 42b Reorder the terms: 14a + -42b + 42b + 7c + -63d = 0 + 42b Combine like terms: -42b + 42b = 0 14a + 0 + 7c + -63d = 0 + 42b 14a + 7c + -63d = 0 + 42b Remove the zero: 14a + 7c + -63d = 42b Add '-7c' to each side of the equation. 14a + 7c + -7c + -63d = 42b + -7c Combine like terms: 7c + -7c = 0 14a + 0 + -63d = 42b + -7c 14a + -63d = 42b + -7c Add '63d' to each side of the equation. 14a + -63d + 63d = 42b + -7c + 63d Combine like terms: -63d + 63d = 0 14a + 0 = 42b + -7c + 63d 14a = 42b + -7c + 63d Divide each side by '14'. a = 3b + -0.5c + 4.5d Simplifying a = 3b + -0.5c + 4.5d
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