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Simplifying 0.06k + -1(k + 0.50) = 0.10(k + 2) Reorder the terms: 0.06k + -1(0.50 + k) = 0.10(k + 2) 0.06k + (0.50 * -1 + k * -1) = 0.10(k + 2) 0.06k + (-0.5 + -1k) = 0.10(k + 2) Reorder the terms: -0.5 + 0.06k + -1k = 0.10(k + 2) Combine like terms: 0.06k + -1k = -0.94k -0.5 + -0.94k = 0.10(k + 2) Reorder the terms: -0.5 + -0.94k = 0.10(2 + k) -0.5 + -0.94k = (2 * 0.10 + k * 0.10) -0.5 + -0.94k = (0.2 + 0.10k) Solving -0.5 + -0.94k = 0.2 + 0.10k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.10k' to each side of the equation. -0.5 + -0.94k + -0.10k = 0.2 + 0.10k + -0.10k Combine like terms: -0.94k + -0.10k = -1.04k -0.5 + -1.04k = 0.2 + 0.10k + -0.10k Combine like terms: 0.10k + -0.10k = 0.00 -0.5 + -1.04k = 0.2 + 0.00 -0.5 + -1.04k = 0.2 Add '0.5' to each side of the equation. -0.5 + 0.5 + -1.04k = 0.2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.04k = 0.2 + 0.5 -1.04k = 0.2 + 0.5 Combine like terms: 0.2 + 0.5 = 0.7 -1.04k = 0.7 Divide each side by '-1.04'. k = -0.6730769231 Simplifying k = -0.6730769231
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