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Simplifying 5(q + 3k) = 4(3k + -5q) + q Reorder the terms: 5(3k + q) = 4(3k + -5q) + q (3k * 5 + q * 5) = 4(3k + -5q) + q (15k + 5q) = 4(3k + -5q) + q 15k + 5q = (3k * 4 + -5q * 4) + q 15k + 5q = (12k + -20q) + q Combine like terms: -20q + q = -19q 15k + 5q = 12k + -19q Solving 15k + 5q = 12k + -19q Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12k' to each side of the equation. 15k + -12k + 5q = 12k + -12k + -19q Combine like terms: 15k + -12k = 3k 3k + 5q = 12k + -12k + -19q Combine like terms: 12k + -12k = 0 3k + 5q = 0 + -19q 3k + 5q = -19q Add '-5q' to each side of the equation. 3k + 5q + -5q = -19q + -5q Combine like terms: 5q + -5q = 0 3k + 0 = -19q + -5q 3k = -19q + -5q Combine like terms: -19q + -5q = -24q 3k = -24q Divide each side by '3'. k = -8q Simplifying k = -8q
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