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Simplifying -13(5k + 22) + 1249 = -597 + -17(10k + -30) Reorder the terms: -13(22 + 5k) + 1249 = -597 + -17(10k + -30) (22 * -13 + 5k * -13) + 1249 = -597 + -17(10k + -30) (-286 + -65k) + 1249 = -597 + -17(10k + -30) Reorder the terms: -286 + 1249 + -65k = -597 + -17(10k + -30) Combine like terms: -286 + 1249 = 963 963 + -65k = -597 + -17(10k + -30) Reorder the terms: 963 + -65k = -597 + -17(-30 + 10k) 963 + -65k = -597 + (-30 * -17 + 10k * -17) 963 + -65k = -597 + (510 + -170k) Combine like terms: -597 + 510 = -87 963 + -65k = -87 + -170k Solving 963 + -65k = -87 + -170k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '170k' to each side of the equation. 963 + -65k + 170k = -87 + -170k + 170k Combine like terms: -65k + 170k = 105k 963 + 105k = -87 + -170k + 170k Combine like terms: -170k + 170k = 0 963 + 105k = -87 + 0 963 + 105k = -87 Add '-963' to each side of the equation. 963 + -963 + 105k = -87 + -963 Combine like terms: 963 + -963 = 0 0 + 105k = -87 + -963 105k = -87 + -963 Combine like terms: -87 + -963 = -1050 105k = -1050 Divide each side by '105'. k = -10 Simplifying k = -10
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