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Simplifying 9(1 + -5k) + -7(-10k + 8) = -97 (1 * 9 + -5k * 9) + -7(-10k + 8) = -97 (9 + -45k) + -7(-10k + 8) = -97 Reorder the terms: 9 + -45k + -7(8 + -10k) = -97 9 + -45k + (8 * -7 + -10k * -7) = -97 9 + -45k + (-56 + 70k) = -97 Reorder the terms: 9 + -56 + -45k + 70k = -97 Combine like terms: 9 + -56 = -47 -47 + -45k + 70k = -97 Combine like terms: -45k + 70k = 25k -47 + 25k = -97 Solving -47 + 25k = -97 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 + 25k = -97 + 47 Combine like terms: -47 + 47 = 0 0 + 25k = -97 + 47 25k = -97 + 47 Combine like terms: -97 + 47 = -50 25k = -50 Divide each side by '25'. k = -2 Simplifying k = -2
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