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Simplifying -64 = -4(8 + -1k) + 7(1 + 5k) -64 = (8 * -4 + -1k * -4) + 7(1 + 5k) -64 = (-32 + 4k) + 7(1 + 5k) -64 = -32 + 4k + (1 * 7 + 5k * 7) -64 = -32 + 4k + (7 + 35k) Reorder the terms: -64 = -32 + 7 + 4k + 35k Combine like terms: -32 + 7 = -25 -64 = -25 + 4k + 35k Combine like terms: 4k + 35k = 39k -64 = -25 + 39k Solving -64 = -25 + 39k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-39k' to each side of the equation. -64 + -39k = -25 + 39k + -39k Combine like terms: 39k + -39k = 0 -64 + -39k = -25 + 0 -64 + -39k = -25 Add '64' to each side of the equation. -64 + 64 + -39k = -25 + 64 Combine like terms: -64 + 64 = 0 0 + -39k = -25 + 64 -39k = -25 + 64 Combine like terms: -25 + 64 = 39 -39k = 39 Divide each side by '-39'. k = -1 Simplifying k = -1
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