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Simplifying 0.50k + -1(k + 0.33) = 0.66(k + 1) Reorder the terms: 0.50k + -1(0.33 + k) = 0.66(k + 1) 0.50k + (0.33 * -1 + k * -1) = 0.66(k + 1) 0.50k + (-0.33 + -1k) = 0.66(k + 1) Reorder the terms: -0.33 + 0.50k + -1k = 0.66(k + 1) Combine like terms: 0.50k + -1k = -0.5k -0.33 + -0.5k = 0.66(k + 1) Reorder the terms: -0.33 + -0.5k = 0.66(1 + k) -0.33 + -0.5k = (1 * 0.66 + k * 0.66) -0.33 + -0.5k = (0.66 + 0.66k) Solving -0.33 + -0.5k = 0.66 + 0.66k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.66k' to each side of the equation. -0.33 + -0.5k + -0.66k = 0.66 + 0.66k + -0.66k Combine like terms: -0.5k + -0.66k = -1.16k -0.33 + -1.16k = 0.66 + 0.66k + -0.66k Combine like terms: 0.66k + -0.66k = 0.00 -0.33 + -1.16k = 0.66 + 0.00 -0.33 + -1.16k = 0.66 Add '0.33' to each side of the equation. -0.33 + 0.33 + -1.16k = 0.66 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + -1.16k = 0.66 + 0.33 -1.16k = 0.66 + 0.33 Combine like terms: 0.66 + 0.33 = 0.99 -1.16k = 0.99 Divide each side by '-1.16'. k = -0.8534482759 Simplifying k = -0.8534482759
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