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Simplifying 0.6k + -1(k + 0.25) = 0.05(k + 1) Reorder the terms: 0.6k + -1(0.25 + k) = 0.05(k + 1) 0.6k + (0.25 * -1 + k * -1) = 0.05(k + 1) 0.6k + (-0.25 + -1k) = 0.05(k + 1) Reorder the terms: -0.25 + 0.6k + -1k = 0.05(k + 1) Combine like terms: 0.6k + -1k = -0.4k -0.25 + -0.4k = 0.05(k + 1) Reorder the terms: -0.25 + -0.4k = 0.05(1 + k) -0.25 + -0.4k = (1 * 0.05 + k * 0.05) -0.25 + -0.4k = (0.05 + 0.05k) Solving -0.25 + -0.4k = 0.05 + 0.05k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.05k' to each side of the equation. -0.25 + -0.4k + -0.05k = 0.05 + 0.05k + -0.05k Combine like terms: -0.4k + -0.05k = -0.45k -0.25 + -0.45k = 0.05 + 0.05k + -0.05k Combine like terms: 0.05k + -0.05k = 0.00 -0.25 + -0.45k = 0.05 + 0.00 -0.25 + -0.45k = 0.05 Add '0.25' to each side of the equation. -0.25 + 0.25 + -0.45k = 0.05 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.45k = 0.05 + 0.25 -0.45k = 0.05 + 0.25 Combine like terms: 0.05 + 0.25 = 0.3 -0.45k = 0.3 Divide each side by '-0.45'. k = -0.6666666667 Simplifying k = -0.6666666667
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