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Simplifying 5k + -5 + 2k + -8 = 4(k + 6) + 2(7k + -2) Reorder the terms: -5 + -8 + 5k + 2k = 4(k + 6) + 2(7k + -2) Combine like terms: -5 + -8 = -13 -13 + 5k + 2k = 4(k + 6) + 2(7k + -2) Combine like terms: 5k + 2k = 7k -13 + 7k = 4(k + 6) + 2(7k + -2) Reorder the terms: -13 + 7k = 4(6 + k) + 2(7k + -2) -13 + 7k = (6 * 4 + k * 4) + 2(7k + -2) -13 + 7k = (24 + 4k) + 2(7k + -2) Reorder the terms: -13 + 7k = 24 + 4k + 2(-2 + 7k) -13 + 7k = 24 + 4k + (-2 * 2 + 7k * 2) -13 + 7k = 24 + 4k + (-4 + 14k) Reorder the terms: -13 + 7k = 24 + -4 + 4k + 14k Combine like terms: 24 + -4 = 20 -13 + 7k = 20 + 4k + 14k Combine like terms: 4k + 14k = 18k -13 + 7k = 20 + 18k Solving -13 + 7k = 20 + 18k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18k' to each side of the equation. -13 + 7k + -18k = 20 + 18k + -18k Combine like terms: 7k + -18k = -11k -13 + -11k = 20 + 18k + -18k Combine like terms: 18k + -18k = 0 -13 + -11k = 20 + 0 -13 + -11k = 20 Add '13' to each side of the equation. -13 + 13 + -11k = 20 + 13 Combine like terms: -13 + 13 = 0 0 + -11k = 20 + 13 -11k = 20 + 13 Combine like terms: 20 + 13 = 33 -11k = 33 Divide each side by '-11'. k = -3 Simplifying k = -3
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