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Simplifying -3(1 + -4k) = 3(-1 + 7k) + -5k (1 * -3 + -4k * -3) = 3(-1 + 7k) + -5k (-3 + 12k) = 3(-1 + 7k) + -5k -3 + 12k = (-1 * 3 + 7k * 3) + -5k -3 + 12k = (-3 + 21k) + -5k Combine like terms: 21k + -5k = 16k -3 + 12k = -3 + 16k Add '3' to each side of the equation. -3 + 3 + 12k = -3 + 3 + 16k Combine like terms: -3 + 3 = 0 0 + 12k = -3 + 3 + 16k 12k = -3 + 3 + 16k Combine like terms: -3 + 3 = 0 12k = 0 + 16k 12k = 16k Solving 12k = 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. 12k + -16k = 16k + -16k Combine like terms: 12k + -16k = -4k -4k = 16k + -16k Combine like terms: 16k + -16k = 0 -4k = 0 Divide each side by '-4'. k = 0 Simplifying k = 0
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