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Simplifying 2k + -1 = -5 + 4(1 + 8k) Reorder the terms: -1 + 2k = -5 + 4(1 + 8k) -1 + 2k = -5 + (1 * 4 + 8k * 4) -1 + 2k = -5 + (4 + 32k) Combine like terms: -5 + 4 = -1 -1 + 2k = -1 + 32k Add '1' to each side of the equation. -1 + 1 + 2k = -1 + 1 + 32k Combine like terms: -1 + 1 = 0 0 + 2k = -1 + 1 + 32k 2k = -1 + 1 + 32k Combine like terms: -1 + 1 = 0 2k = 0 + 32k 2k = 32k Solving 2k = 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. 2k + -32k = 32k + -32k Combine like terms: 2k + -32k = -30k -30k = 32k + -32k Combine like terms: 32k + -32k = 0 -30k = 0 Divide each side by '-30'. k = 0.0 Simplifying k = 0.0
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