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Simplifying 0.5k + -1(k + 0.33) = 0.16(k + 3) Reorder the terms: 0.5k + -1(0.33 + k) = 0.16(k + 3) 0.5k + (0.33 * -1 + k * -1) = 0.16(k + 3) 0.5k + (-0.33 + -1k) = 0.16(k + 3) Reorder the terms: -0.33 + 0.5k + -1k = 0.16(k + 3) Combine like terms: 0.5k + -1k = -0.5k -0.33 + -0.5k = 0.16(k + 3) Reorder the terms: -0.33 + -0.5k = 0.16(3 + k) -0.33 + -0.5k = (3 * 0.16 + k * 0.16) -0.33 + -0.5k = (0.48 + 0.16k) Solving -0.33 + -0.5k = 0.48 + 0.16k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.16k' to each side of the equation. -0.33 + -0.5k + -0.16k = 0.48 + 0.16k + -0.16k Combine like terms: -0.5k + -0.16k = -0.66k -0.33 + -0.66k = 0.48 + 0.16k + -0.16k Combine like terms: 0.16k + -0.16k = 0.00 -0.33 + -0.66k = 0.48 + 0.00 -0.33 + -0.66k = 0.48 Add '0.33' to each side of the equation. -0.33 + 0.33 + -0.66k = 0.48 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + -0.66k = 0.48 + 0.33 -0.66k = 0.48 + 0.33 Combine like terms: 0.48 + 0.33 = 0.81 -0.66k = 0.81 Divide each side by '-0.66'. k = -1.227272727 Simplifying k = -1.227272727
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