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Simplifying 2(4q + k) + -6(3p + -1q) = 0 Reorder the terms: 2(k + 4q) + -6(3p + -1q) = 0 (k * 2 + 4q * 2) + -6(3p + -1q) = 0 (2k + 8q) + -6(3p + -1q) = 0 2k + 8q + (3p * -6 + -1q * -6) = 0 2k + 8q + (-18p + 6q) = 0 Reorder the terms: 2k + -18p + 8q + 6q = 0 Combine like terms: 8q + 6q = 14q 2k + -18p + 14q = 0 Solving 2k + -18p + 14q = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '18p' to each side of the equation. 2k + -18p + 18p + 14q = 0 + 18p Combine like terms: -18p + 18p = 0 2k + 0 + 14q = 0 + 18p 2k + 14q = 0 + 18p Remove the zero: 2k + 14q = 18p Add '-14q' to each side of the equation. 2k + 14q + -14q = 18p + -14q Combine like terms: 14q + -14q = 0 2k + 0 = 18p + -14q 2k = 18p + -14q Divide each side by '2'. k = 9p + -7q Simplifying k = 9p + -7q
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