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Simplifying 2(1 + 5k) + -3(10 + 8k) = -8k + 1k (1 * 2 + 5k * 2) + -3(10 + 8k) = -8k + 1k (2 + 10k) + -3(10 + 8k) = -8k + 1k 2 + 10k + (10 * -3 + 8k * -3) = -8k + 1k 2 + 10k + (-30 + -24k) = -8k + 1k Reorder the terms: 2 + -30 + 10k + -24k = -8k + 1k Combine like terms: 2 + -30 = -28 -28 + 10k + -24k = -8k + 1k Combine like terms: 10k + -24k = -14k -28 + -14k = -8k + 1k Combine like terms: -8k + 1k = -7k -28 + -14k = -7k Solving -28 + -14k = -7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7k' to each side of the equation. -28 + -14k + 7k = -7k + 7k Combine like terms: -14k + 7k = -7k -28 + -7k = -7k + 7k Combine like terms: -7k + 7k = 0 -28 + -7k = 0 Add '28' to each side of the equation. -28 + 28 + -7k = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -7k = 0 + 28 -7k = 0 + 28 Combine like terms: 0 + 28 = 28 -7k = 28 Divide each side by '-7'. k = -4 Simplifying k = -4
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