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Simplifying 6(5 + 7k) + 2 = 4k + 32 (5 * 6 + 7k * 6) + 2 = 4k + 32 (30 + 42k) + 2 = 4k + 32 Reorder the terms: 30 + 2 + 42k = 4k + 32 Combine like terms: 30 + 2 = 32 32 + 42k = 4k + 32 Reorder the terms: 32 + 42k = 32 + 4k Add '-32' to each side of the equation. 32 + -32 + 42k = 32 + -32 + 4k Combine like terms: 32 + -32 = 0 0 + 42k = 32 + -32 + 4k 42k = 32 + -32 + 4k Combine like terms: 32 + -32 = 0 42k = 0 + 4k 42k = 4k Solving 42k = 4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4k' to each side of the equation. 42k + -4k = 4k + -4k Combine like terms: 42k + -4k = 38k 38k = 4k + -4k Combine like terms: 4k + -4k = 0 38k = 0 Divide each side by '38'. k = 0 Simplifying k = 0
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