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Simplifying 0.5(6k + -0.5) + -0.5(3k + -0.25) + -0.8(5k + -2) = 0 Reorder the terms: 0.5(-0.5 + 6k) + -0.5(3k + -0.25) + -0.8(5k + -2) = 0 (-0.5 * 0.5 + 6k * 0.5) + -0.5(3k + -0.25) + -0.8(5k + -2) = 0 (-0.25 + 3k) + -0.5(3k + -0.25) + -0.8(5k + -2) = 0 Reorder the terms: -0.25 + 3k + -0.5(-0.25 + 3k) + -0.8(5k + -2) = 0 -0.25 + 3k + (-0.25 * -0.5 + 3k * -0.5) + -0.8(5k + -2) = 0 -0.25 + 3k + (0.125 + -1.5k) + -0.8(5k + -2) = 0 Reorder the terms: -0.25 + 3k + 0.125 + -1.5k + -0.8(-2 + 5k) = 0 -0.25 + 3k + 0.125 + -1.5k + (-2 * -0.8 + 5k * -0.8) = 0 -0.25 + 3k + 0.125 + -1.5k + (1.6 + -4k) = 0 Reorder the terms: -0.25 + 0.125 + 1.6 + 3k + -1.5k + -4k = 0 Combine like terms: -0.25 + 0.125 = -0.125 -0.125 + 1.6 + 3k + -1.5k + -4k = 0 Combine like terms: -0.125 + 1.6 = 1.475 1.475 + 3k + -1.5k + -4k = 0 Combine like terms: 3k + -1.5k = 1.5k 1.475 + 1.5k + -4k = 0 Combine like terms: 1.5k + -4k = -2.5k 1.475 + -2.5k = 0 Solving 1.475 + -2.5k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.475' to each side of the equation. 1.475 + -1.475 + -2.5k = 0 + -1.475 Combine like terms: 1.475 + -1.475 = 0.000 0.000 + -2.5k = 0 + -1.475 -2.5k = 0 + -1.475 Combine like terms: 0 + -1.475 = -1.475 -2.5k = -1.475 Divide each side by '-2.5'. k = 0.59 Simplifying k = 0.59
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