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Simplifying 4(7 + 7k) = 8(1 + 3k) (7 * 4 + 7k * 4) = 8(1 + 3k) (28 + 28k) = 8(1 + 3k) 28 + 28k = (1 * 8 + 3k * 8) 28 + 28k = (8 + 24k) Solving 28 + 28k = 8 + 24k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-24k' to each side of the equation. 28 + 28k + -24k = 8 + 24k + -24k Combine like terms: 28k + -24k = 4k 28 + 4k = 8 + 24k + -24k Combine like terms: 24k + -24k = 0 28 + 4k = 8 + 0 28 + 4k = 8 Add '-28' to each side of the equation. 28 + -28 + 4k = 8 + -28 Combine like terms: 28 + -28 = 0 0 + 4k = 8 + -28 4k = 8 + -28 Combine like terms: 8 + -28 = -20 4k = -20 Divide each side by '4'. k = -5 Simplifying k = -5
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