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Simplifying 9(1 + -5k) + -11(k + 7) = 100 (1 * 9 + -5k * 9) + -11(k + 7) = 100 (9 + -45k) + -11(k + 7) = 100 Reorder the terms: 9 + -45k + -11(7 + k) = 100 9 + -45k + (7 * -11 + k * -11) = 100 9 + -45k + (-77 + -11k) = 100 Reorder the terms: 9 + -77 + -45k + -11k = 100 Combine like terms: 9 + -77 = -68 -68 + -45k + -11k = 100 Combine like terms: -45k + -11k = -56k -68 + -56k = 100 Solving -68 + -56k = 100 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '68' to each side of the equation. -68 + 68 + -56k = 100 + 68 Combine like terms: -68 + 68 = 0 0 + -56k = 100 + 68 -56k = 100 + 68 Combine like terms: 100 + 68 = 168 -56k = 168 Divide each side by '-56'. k = -3 Simplifying k = -3
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