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Simplifying 0.75k + -1(k + 0.5) = 0.125(k + 1) Reorder the terms: 0.75k + -1(0.5 + k) = 0.125(k + 1) 0.75k + (0.5 * -1 + k * -1) = 0.125(k + 1) 0.75k + (-0.5 + -1k) = 0.125(k + 1) Reorder the terms: -0.5 + 0.75k + -1k = 0.125(k + 1) Combine like terms: 0.75k + -1k = -0.25k -0.5 + -0.25k = 0.125(k + 1) Reorder the terms: -0.5 + -0.25k = 0.125(1 + k) -0.5 + -0.25k = (1 * 0.125 + k * 0.125) -0.5 + -0.25k = (0.125 + 0.125k) Solving -0.5 + -0.25k = 0.125 + 0.125k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.125k' to each side of the equation. -0.5 + -0.25k + -0.125k = 0.125 + 0.125k + -0.125k Combine like terms: -0.25k + -0.125k = -0.375k -0.5 + -0.375k = 0.125 + 0.125k + -0.125k Combine like terms: 0.125k + -0.125k = 0.000 -0.5 + -0.375k = 0.125 + 0.000 -0.5 + -0.375k = 0.125 Add '0.5' to each side of the equation. -0.5 + 0.5 + -0.375k = 0.125 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.375k = 0.125 + 0.5 -0.375k = 0.125 + 0.5 Combine like terms: 0.125 + 0.5 = 0.625 -0.375k = 0.625 Divide each side by '-0.375'. k = -1.666666667 Simplifying k = -1.666666667
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