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Simplifying 4(4k + 1) + -8(k + -1) = 3(25k + 2) + -2 Reorder the terms: 4(1 + 4k) + -8(k + -1) = 3(25k + 2) + -2 (1 * 4 + 4k * 4) + -8(k + -1) = 3(25k + 2) + -2 (4 + 16k) + -8(k + -1) = 3(25k + 2) + -2 Reorder the terms: 4 + 16k + -8(-1 + k) = 3(25k + 2) + -2 4 + 16k + (-1 * -8 + k * -8) = 3(25k + 2) + -2 4 + 16k + (8 + -8k) = 3(25k + 2) + -2 Reorder the terms: 4 + 8 + 16k + -8k = 3(25k + 2) + -2 Combine like terms: 4 + 8 = 12 12 + 16k + -8k = 3(25k + 2) + -2 Combine like terms: 16k + -8k = 8k 12 + 8k = 3(25k + 2) + -2 Reorder the terms: 12 + 8k = 3(2 + 25k) + -2 12 + 8k = (2 * 3 + 25k * 3) + -2 12 + 8k = (6 + 75k) + -2 Reorder the terms: 12 + 8k = 6 + -2 + 75k Combine like terms: 6 + -2 = 4 12 + 8k = 4 + 75k Solving 12 + 8k = 4 + 75k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-75k' to each side of the equation. 12 + 8k + -75k = 4 + 75k + -75k Combine like terms: 8k + -75k = -67k 12 + -67k = 4 + 75k + -75k Combine like terms: 75k + -75k = 0 12 + -67k = 4 + 0 12 + -67k = 4 Add '-12' to each side of the equation. 12 + -12 + -67k = 4 + -12 Combine like terms: 12 + -12 = 0 0 + -67k = 4 + -12 -67k = 4 + -12 Combine like terms: 4 + -12 = -8 -67k = -8 Divide each side by '-67'. k = 0.1194029851 Simplifying k = 0.1194029851
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