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Simplifying -5k + -7 + k + -5 = 8(2k + -7) + 5(-4K + 5) Reorder the terms: -7 + -5 + -5k + k = 8(2k + -7) + 5(-4K + 5) Combine like terms: -7 + -5 = -12 -12 + -5k + k = 8(2k + -7) + 5(-4K + 5) Combine like terms: -5k + k = -4k -12 + -4k = 8(2k + -7) + 5(-4K + 5) Reorder the terms: -12 + -4k = 8(-7 + 2k) + 5(-4K + 5) -12 + -4k = (-7 * 8 + 2k * 8) + 5(-4K + 5) -12 + -4k = (-56 + 16k) + 5(-4K + 5) Reorder the terms: -12 + -4k = -56 + 16k + 5(5 + -4K) -12 + -4k = -56 + 16k + (5 * 5 + -4K * 5) -12 + -4k = -56 + 16k + (25 + -20K) Reorder the terms: -12 + -4k = -56 + 25 + -20K + 16k Combine like terms: -56 + 25 = -31 -12 + -4k = -31 + -20K + 16k Solving -12 + -4k = -31 + -20K + 16k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-16k' to each side of the equation. -12 + -4k + -16k = -31 + -20K + 16k + -16k Combine like terms: -4k + -16k = -20k -12 + -20k = -31 + -20K + 16k + -16k Combine like terms: 16k + -16k = 0 -12 + -20k = -31 + -20K + 0 -12 + -20k = -31 + -20K Add '12' to each side of the equation. -12 + 12 + -20k = -31 + 12 + -20K Combine like terms: -12 + 12 = 0 0 + -20k = -31 + 12 + -20K -20k = -31 + 12 + -20K Combine like terms: -31 + 12 = -19 -20k = -19 + -20K Divide each side by '-20'. k = 0.95 + K Simplifying k = 0.95 + K
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