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Simplifying 0.3k + -0.075 + k = -6(-1k + 1) + 0.05 Reorder the terms: -0.075 + 0.3k + k = -6(-1k + 1) + 0.05 Combine like terms: 0.3k + k = 1.3k -0.075 + 1.3k = -6(-1k + 1) + 0.05 Reorder the terms: -0.075 + 1.3k = -6(1 + -1k) + 0.05 -0.075 + 1.3k = (1 * -6 + -1k * -6) + 0.05 -0.075 + 1.3k = (-6 + 6k) + 0.05 Reorder the terms: -0.075 + 1.3k = -6 + 0.05 + 6k Combine like terms: -6 + 0.05 = -5.95 -0.075 + 1.3k = -5.95 + 6k Solving -0.075 + 1.3k = -5.95 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. -0.075 + 1.3k + -6k = -5.95 + 6k + -6k Combine like terms: 1.3k + -6k = -4.7k -0.075 + -4.7k = -5.95 + 6k + -6k Combine like terms: 6k + -6k = 0 -0.075 + -4.7k = -5.95 + 0 -0.075 + -4.7k = -5.95 Add '0.075' to each side of the equation. -0.075 + 0.075 + -4.7k = -5.95 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + -4.7k = -5.95 + 0.075 -4.7k = -5.95 + 0.075 Combine like terms: -5.95 + 0.075 = -5.875 -4.7k = -5.875 Divide each side by '-4.7'. k = 1.25 Simplifying k = 1.25
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