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Simplifying -7(-6 + -3k) + 5(1 + 3k) = 0 (-6 * -7 + -3k * -7) + 5(1 + 3k) = 0 (42 + 21k) + 5(1 + 3k) = 0 42 + 21k + (1 * 5 + 3k * 5) = 0 42 + 21k + (5 + 15k) = 0 Reorder the terms: 42 + 5 + 21k + 15k = 0 Combine like terms: 42 + 5 = 47 47 + 21k + 15k = 0 Combine like terms: 21k + 15k = 36k 47 + 36k = 0 Solving 47 + 36k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-47' to each side of the equation. 47 + -47 + 36k = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 36k = 0 + -47 36k = 0 + -47 Combine like terms: 0 + -47 = -47 36k = -47 Divide each side by '36'. k = -1.305555556 Simplifying k = -1.305555556
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