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Simplifying 4(-1 + 7k) + -4(1 + 6k) = 2k + 3k (-1 * 4 + 7k * 4) + -4(1 + 6k) = 2k + 3k (-4 + 28k) + -4(1 + 6k) = 2k + 3k -4 + 28k + (1 * -4 + 6k * -4) = 2k + 3k -4 + 28k + (-4 + -24k) = 2k + 3k Reorder the terms: -4 + -4 + 28k + -24k = 2k + 3k Combine like terms: -4 + -4 = -8 -8 + 28k + -24k = 2k + 3k Combine like terms: 28k + -24k = 4k -8 + 4k = 2k + 3k Combine like terms: 2k + 3k = 5k -8 + 4k = 5k Solving -8 + 4k = 5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5k' to each side of the equation. -8 + 4k + -5k = 5k + -5k Combine like terms: 4k + -5k = -1k -8 + -1k = 5k + -5k Combine like terms: 5k + -5k = 0 -8 + -1k = 0 Add '8' to each side of the equation. -8 + 8 + -1k = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1k = 0 + 8 -1k = 0 + 8 Combine like terms: 0 + 8 = 8 -1k = 8 Divide each side by '-1'. k = -8 Simplifying k = -8
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