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Simplifying 5(5 + -1k) = 8(4 + -4k) (5 * 5 + -1k * 5) = 8(4 + -4k) (25 + -5k) = 8(4 + -4k) 25 + -5k = (4 * 8 + -4k * 8) 25 + -5k = (32 + -32k) Solving 25 + -5k = 32 + -32k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '32k' to each side of the equation. 25 + -5k + 32k = 32 + -32k + 32k Combine like terms: -5k + 32k = 27k 25 + 27k = 32 + -32k + 32k Combine like terms: -32k + 32k = 0 25 + 27k = 32 + 0 25 + 27k = 32 Add '-25' to each side of the equation. 25 + -25 + 27k = 32 + -25 Combine like terms: 25 + -25 = 0 0 + 27k = 32 + -25 27k = 32 + -25 Combine like terms: 32 + -25 = 7 27k = 7 Divide each side by '27'. k = 0.2592592593 Simplifying k = 0.2592592593
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