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Simplifying 0.5k + -1(k + 0.5) = 0.25k + 2 Reorder the terms: 0.5k + -1(0.5 + k) = 0.25k + 2 0.5k + (0.5 * -1 + k * -1) = 0.25k + 2 0.5k + (-0.5 + -1k) = 0.25k + 2 Reorder the terms: -0.5 + 0.5k + -1k = 0.25k + 2 Combine like terms: 0.5k + -1k = -0.5k -0.5 + -0.5k = 0.25k + 2 Reorder the terms: -0.5 + -0.5k = 2 + 0.25k Solving -0.5 + -0.5k = 2 + 0.25k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.25k' to each side of the equation. -0.5 + -0.5k + -0.25k = 2 + 0.25k + -0.25k Combine like terms: -0.5k + -0.25k = -0.75k -0.5 + -0.75k = 2 + 0.25k + -0.25k Combine like terms: 0.25k + -0.25k = 0.00 -0.5 + -0.75k = 2 + 0.00 -0.5 + -0.75k = 2 Add '0.5' to each side of the equation. -0.5 + 0.5 + -0.75k = 2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.75k = 2 + 0.5 -0.75k = 2 + 0.5 Combine like terms: 2 + 0.5 = 2.5 -0.75k = 2.5 Divide each side by '-0.75'. k = -3.333333333 Simplifying k = -3.333333333
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