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Simplifying 5(7 + -1k) + 70(k + -9) = 1 (7 * 5 + -1k * 5) + 70(k + -9) = 1 (35 + -5k) + 70(k + -9) = 1 Reorder the terms: 35 + -5k + 70(-9 + k) = 1 35 + -5k + (-9 * 70 + k * 70) = 1 35 + -5k + (-630 + 70k) = 1 Reorder the terms: 35 + -630 + -5k + 70k = 1 Combine like terms: 35 + -630 = -595 -595 + -5k + 70k = 1 Combine like terms: -5k + 70k = 65k -595 + 65k = 1 Solving -595 + 65k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '595' to each side of the equation. -595 + 595 + 65k = 1 + 595 Combine like terms: -595 + 595 = 0 0 + 65k = 1 + 595 65k = 1 + 595 Combine like terms: 1 + 595 = 596 65k = 596 Divide each side by '65'. k = 9.169230769 Simplifying k = 9.169230769
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