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Simplifying 5 + -1(6k + 1) = 2((5k + -3) + -1(K + -2)) Reorder the terms: 5 + -1(1 + 6k) = 2((5k + -3) + -1(K + -2)) 5 + (1 * -1 + 6k * -1) = 2((5k + -3) + -1(K + -2)) 5 + (-1 + -6k) = 2((5k + -3) + -1(K + -2)) Combine like terms: 5 + -1 = 4 4 + -6k = 2((5k + -3) + -1(K + -2)) Reorder the terms: 4 + -6k = 2((-3 + 5k) + -1(K + -2)) Remove parenthesis around (-3 + 5k) 4 + -6k = 2(-3 + 5k + -1(K + -2)) Reorder the terms: 4 + -6k = 2(-3 + 5k + -1(-2 + K)) 4 + -6k = 2(-3 + 5k + (-2 * -1 + K * -1)) 4 + -6k = 2(-3 + 5k + (2 + -1K)) Reorder the terms: 4 + -6k = 2(-3 + 2 + -1K + 5k) Combine like terms: -3 + 2 = -1 4 + -6k = 2(-1 + -1K + 5k) 4 + -6k = (-1 * 2 + -1K * 2 + 5k * 2) 4 + -6k = (-2 + -2K + 10k) Solving 4 + -6k = -2 + -2K + 10k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10k' to each side of the equation. 4 + -6k + -10k = -2 + -2K + 10k + -10k Combine like terms: -6k + -10k = -16k 4 + -16k = -2 + -2K + 10k + -10k Combine like terms: 10k + -10k = 0 4 + -16k = -2 + -2K + 0 4 + -16k = -2 + -2K Add '-4' to each side of the equation. 4 + -4 + -16k = -2 + -4 + -2K Combine like terms: 4 + -4 = 0 0 + -16k = -2 + -4 + -2K -16k = -2 + -4 + -2K Combine like terms: -2 + -4 = -6 -16k = -6 + -2K Divide each side by '-16'. k = 0.375 + 0.125K Simplifying k = 0.375 + 0.125K
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