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Simplifying 0.2(15k + -1.5) = 0.5(7.5 + -3k) Reorder the terms: 0.2(-1.5 + 15k) = 0.5(7.5 + -3k) (-1.5 * 0.2 + 15k * 0.2) = 0.5(7.5 + -3k) (-0.3 + 3k) = 0.5(7.5 + -3k) -0.3 + 3k = (7.5 * 0.5 + -3k * 0.5) -0.3 + 3k = (3.75 + -1.5k) Solving -0.3 + 3k = 3.75 + -1.5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5k' to each side of the equation. -0.3 + 3k + 1.5k = 3.75 + -1.5k + 1.5k Combine like terms: 3k + 1.5k = 4.5k -0.3 + 4.5k = 3.75 + -1.5k + 1.5k Combine like terms: -1.5k + 1.5k = 0.0 -0.3 + 4.5k = 3.75 + 0.0 -0.3 + 4.5k = 3.75 Add '0.3' to each side of the equation. -0.3 + 0.3 + 4.5k = 3.75 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 4.5k = 3.75 + 0.3 4.5k = 3.75 + 0.3 Combine like terms: 3.75 + 0.3 = 4.05 4.5k = 4.05 Divide each side by '4.5'. k = 0.9 Simplifying k = 0.9
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